Introduction
Femicide is, unfortunately, all but a new phenomenon. What is new, however, is the increased recognition of its global character and the growing use of the term. Although there is not one single, universally accepted definition of femicide, it is generally described in scholarly literature as the gender-based murder of a woman. Despite femicide’s gravity, most states crucially lack specific legislation criminalizing this crime, and existing laws often fail to capture and address the misogynistic underpinnings of violence against women (VAW). Similarly, international law also lacks explicit provisions on femicide. This gap reflects the field’s historical difficulties in translating the protection of women’s rights into effective and binding international legal instruments. As Otto points out, international institutions, especially courts and tribunals, significantly struggle to adjudicate femicide as well as other forms of systemic VAW.
In light of the scant existing legislation, this Essay argues that international law should seek to fill this gap to eradicate—or at least substantially reduce—femicide as an ancient, structural, global problem. International criminal law, in particular, can play a pivotal role by imposing precise international obligations upon states to promote greater state accountability. Among others, one significant area where international regulation could make a substantial impact is the international fight against femicide. A legally binding international framework on femicide could drive state intervention on VAW and offer more effective responses to femicide’s alarming rate.
The topic of femicide in international law is both timely and crucial for this Symposium because femicide is a pervasive global issue that eminently reveals the severe violence that all women face solely due to their gender. Despite the existence of several international agreements aimed at protecting women’s rights, the absence of a binding international framework on femicide leaves significant gaps in justice and accountability. This Symposium provides a unique platform to discuss the introduction of such a legal framework, one that could dramatically improve international law’s ability to prevent, prosecute, and eradicate femicide. Furthermore, recent cases and statistics—especially from regions such as Latin America—underscore the urgency of action addressing this global issue.
At the international law level, the issue of VAW is increasingly gaining attention, as evidenced by the ongoing debatearound a potential Optional Protocol to the Convention on the Elimination of All Forms of Discrimination Against Women (CEDAW) and the recent approval by the European Parliament of the Directive 2024/1385,which calls for stronger laws on combating VAW and domestic violence. While at first glance, it may appear that sufficient laws have been enacted both nationally and internationally to protect women’s rights, the critical question remains: how are they enforced? Women’s rights, in fact, continue to face significant obstacles worldwide, often shaped by entrenched gender stereotypes and patriarchal attitudes toward women’s roles in society.
A caveat is necessary in this regard. This Essay acknowledges that international criminal law cannot be the sole solution to femicide. Law per se does not guarantee the eradication of a phenomenon. Eradication requires a broader cultural shift. Nevertheless, new legal instruments are essential to recognize and protect a common fundamental value—here, women’s right to life. That is to say, just because the current laws are inefficient does not mean that we should discard the importance of law itself, especially given that the ultimate aim of criminal law is not to impose a penalty or a punishment but, broadly speaking, general prevention.
This Essay’s analysis unfolds in three parts. First, it describes the global scale and nature of femicide as a structural issue, offering an overview of the phenomenon, its definition, and its prevalence. Second, it critically examines the state of international law on femicide, identifying key normative gaps and challenges faced by international institutions. Finally, it proposes the development of a new international legal framework specifically addressing femicide, drawing inspiration from domestic criminal legislation in Latin America, and outlines the potential elements of such a framework. The latter could significantly enhance state accountability and contribute to global efforts to eradicate VAW.
I. Understanding Femicide
The term “femicide” has deep historical roots, with early variants of this word having existed in France, Italy, and the United States as far back as the seventeenth century. Still, its widespread usage only took hold in the twentieth century. The sociologist Diana Russell mentioned it for the first time at the 1976 International Tribunal on Crimes against Women in Brussels, Belgium, but it did not become widely recognized until later. A decisive moment for the diffusion of the term in feminist discourse was the publication of Russell and Redford’s 1992 book Femicide: The Politics of Woman Killing. The authors defined femicide as the misogynist killing of women by men and as the most extreme manifestation of the continuum of violence against women. For Russell and Redford, naming the crime as “femicide” was key to acknowledging it as an inherently political matter, thus requiring intervention by public institutions.
While primarily focusing on male-perpetrated femicide, the term can encompass killings committed or facilitated by women that are motivated by misogyny. These forms of femicide include, among others, intimate-partner femicide in lesbian couples, honor-related killings, and deaths resulting from harmful practices such as female genital mutilation. For example, in Mexican law, femicide refers to the killing of a female victim. This specification is not intended to discriminate against men but rather to provide an additional layer of protection for women, who are disproportionately vulnerable to homicidal violence. Furthermore, the term femicide typically refers to the cisgender male-female binary, but femicide’s victims can include non-binary, non-heteronormative, intersex, and many other women. The question of what constitutes a “woman” in international lawremains the subject of ongoing feminist legal debates.
The lack of femicide regulation in international law has led to numerous different interpretations. Following Corn’s work, this Essay suggests conceptualizing femicide as gender-based violence resulting in the killing of a woman. However, for many authors, including Mexican politician Lagarde, the definition should extend beyond the act of killing because femicide usually occurs after a series of violent acts against the victim, making the murder merely the final, most extreme stage of the continuum of violence.
Notably, femicide differs from genocide as defined in Article II of the Genocide Convention, as it does not require an intent to exterminate all women to qualify as such. Although femicide perpetrators are primarily driven by misogyny, their intent is usually to eliminate that individual victim, not to destroy all women. And, even if one considers women as a “group” for the Genocide Convention, great difficulty exists in proving the subjective element of the crime, namely the intention of destroying the female gender, as well as the existence of a similar policy.
Femicide is a form of VAW, but not all acts of VAW qualify as femicide. Unlike homicide, which is the unlawful killing of an individual regardless of their gender, femicide stems from misogynistic attitudes that devalue a woman’s life. It often occurs within the context of intimate partner violence, where women are killed by their former or current partners, but it can also include killings related to honor-based violence and targeted attacks against women in armed conflict. The term “femicide” precisely indicates the gendered nature of these killings, distinguishing them from general homicide.
Recognizing femicide as a separate category of crime is essential for developing adequate legal and policy measures to prevent this type of murder and hold perpetrators accountable. Addressing femicide requires not only criminal justice responses but also a broader societal shift to dismantle the patriarchal social and legal norms that underlie and sometimes sustain this form of VAW.
According to recent studies, the leading cause of women’s deaths in the world is not car accidents, cancer, or famine, but homicide. A significant portion of these homicides are femicides , meaning that the majority of homicide’s female victims are killed because of their gender. These killings are not isolated incidents but are inextricably intertwined with systemic gender-related discrimination.
The latest UNODC data reveals that while the overall homicide rate sharply decreased in most countries over the past few years, the rate of femicide remained steady, failing to benefit from this downward trend. In all regions of the world, gender-based violence disproportionately affects women. This aspect gains particular importance if read in conjunction with data on intimate-partner homicides, in which 66% of victims are female. According to the UNODC data, in 2022, approximately 87,000 women were intentionally killed, of which 48,000 were killed by their intimate partners or other family members. This statistic reveals a significant gender disparity, indicating that women are more frequently targeted in domestic settings. The fact that a large percentage of killings of women occur at the hands of their intimate partners highlights a specific pattern. Intimate partner violence is typically rooted in gender power imbalances and patriarchal attitudes that consistently devalue female lives or perpetuate harmful stereotypes about women. Therefore, it is safe to infer that most killings of women and girls are gender motivated.
Further, Latin America presents a particular challenge, with countries like El Salvador, Honduras, and Mexico reporting some of the highest femicide rates globally. In Mexico, the ongoing femicide crisis has led to widespread protests and demands for justice, as exemplified by the high-profile case of Ingrid Escamilla, whose brutal murder in 2020 sparked national outrage and highlighted the systemic failure to protect women. These statistics and examples underscore the global prevalence and devastating impact of femicide, reinforcing the necessity for targeted international legal frameworks to address and prevent this egregious violation of women’s right to life.
II. Femicide in International Law
Femicide is not only a personal tragedy but also a societal issue that reflects broader structural inequalities and systemic failures to adequately protect women. The international community has recognized the severity of gender-based violence through various legal instruments, such as the 1979 Convention on the Elimination of All Forms of Discrimination Against Women (CEDAW). However, considerable gaps remain in terms of the protection of women’s rights, especially when it comes to addressing femicide.
Manjoo and Jones argue that the current international legal framework on VAW is woefully insufficient, fragmented, and outdated. In particular, it lacks specific provisions that expressly recognize and criminalize femicide as a stand-alone offense, leaving a significant gap in women’s protection under international law. Normative voids like this result in inconsistent and vague definitions, uneven protection regimes, and inadequate enforcement mechanisms across jurisdictions.
At the UN level, CEDAW is the only legally binding instrument addressing discrimination against women, but as mentioned above, it sadly fails to directly address VAW, let alone femicide. While the CEDAW Committee, which monitors the treaty’s implementation, has provided evolutive interpretations of the Convention through its thirty-nine general recommendations, these are not legally binding and do not fill the treaty’s gap regarding explicit protection against femicide.
Further complicating the issue, as Latino points out, several state parties formulated a high number of reservations to CEDAW that are in sooth incompatible with the object and purpose of the treaty, thereby dampening its preceptive potential to advance women’s rights. Other states, such as Iran and the United States, have not even ratified the Convention. States such as Egypt and Libya have filed reservations to the CEDAW, claiming that provisions on gender equality in marriage overtly clash with their interpretation of Islamic rules that already provide a balance between the rights and duties of spouses.
Outside of the human rights sphere, other branches of international law fail to address femicide as a specific, gender-based crime. Among others, international criminal law usually addresses VAW only when related to core international crimes, namely crimes against humanity, genocide, and war crimes. Although femicide could theoretically be prosecuted under each of these categories, their definitions and contextual elements render them inconsistent with the legal nature of femicide.
For instance, the definition of crimes against humanity in the Rome Statute of the International Criminal Court requires that the crime occurs as part of a “widespread or systematic attack against a civilian population.” Besides there possibly being an additional and different discussion on whether women could constitute a civilian population in the sense of crimes against humanity, femicides are rarely committed in such a “widespread or systematic attack”. Therefore, the categorization of femicide as only an underlying offense for a crime against humanity would exclude most femicides, as they typically occur in intimate-partner or familial contexts rather than as part of large-scale attacks.
III. Regional Approaches
At the regional level, only Latin America and Europe have adopted important conventions specifically on VAW (i.e., the Belem do Para Convention (1994) and the Istanbul Convention (2011)). Indubitably, both play the prizeworthy role of shedding light on and regulating various forms of VAW; however, they only bind a limited number of states—hence, they are not universal treaties. Also, both conventions lack coercive enforcement mechanisms, leaving a significant margin of discretion to states in implementing their provisions. This lack of enforceability limits the impact of these conventions and has been a point of critique, particularly when states fail to adequately address femicide and other forms of VAW.
Despite its limits, CEDAW markedly laid the foundations for subsequent similar conventions, in particular the Belem do Para Convention, adopted in 1994 by the Organization of American States. This treaty was a landmark because, for the first time, a binding legal instrument expressly provided a definition of VAW as a violation of human rights. This is key to comprehending the strong link between gender inequality and the state’s deficiencies in respecting its due diligence obligations in the protection of human rights.
Although the Convention plays a key role in the protection of women’s rights, it has some intrinsic limitations. One of the most striking problems is the absence of coercive enforcement mechanisms which guarantee the Convention’s implementation by states parties and sanction them if needed. As reported by the Follow Up Mechanism of the 1994 Convention, the effort to counteract VAW relies entirely on the Inter-American Court of Human Rights, and parties are still not willing to bear international responsibility for their numerous failures in human rights protection. The inaction of governments and national authorities in several cases of femicide demonstrates that the Convention did not promote a radical change in VAW’s rates.
By comparison, the European legal framework is more fragmented, and no country has expressly codified femicide. The Istanbul Convention addresses VAW comprehensively but has faced criticism for its failure to adopt an intersectional perspective to VAW, and for essentializing certain forms of VAW as culture specific, indirectly blaming non-Western societies. As Peroni aptly recognizes, this failure undermines the convention’s credibility and effectiveness in ensuring protection for women.
Besides, the European Convention on Human Rights (ECHR) is the main legal instrument that guarantees at the regional level the protection of human rights. However, it only contains limited provisions on gender equality, and they primarily refer to the right to non-discrimination (Article 14) and to heterosexual marriage (Article 16). These provisions do not directly address femicide or specific forms of VAW.
Lastly, international and regional courts that adjudicate VAW cases often rely on general provisions, such as the prohibition of discrimination, to address various forms of gender-based violence. While this is not a problematic interpretation per se (especially considering the absence of other specific legal categories), it tends to overlook the specificity of gender-based crimes like femicide, and may indirectly downgrade gender issues, rather than addressing them as a form of violence rooted in misogyny.
IV. The Need for a New International Legal Framework
Existing international legal instruments concerning women’s rights, such as CEDAW, broadly address gender-based violence but fail to single out femicide as a distinct, egregious crime. This omission represents a failure of the whole international community given that femicide is rooted in widespread misogynistic attitudes and structural inequalities that transcend national borders, and lead to gender-based violence in every area of the world.
By explicitly recognizing femicide as a distinct crime, international law can more effectively highlight the gravity of the related offense and the specific societal and systemic issues that dramatically favor it. Such recognition would also help standardize definitions and enforcement mechanisms globally, ensuring that all countries adopt a consistent approach to preventing and punishing femicide.
While individual criminal responsibility may be included, the focus of the proposed legal framework would be on states’ obligations to criminalize femicide in order to better prevent it. For this purpose, investigation and prosecution efforts should be strengthened with states required to provide full reparations to victims’ families, including compensation, rehabilitation, and guarantees of non-repetition. Along the same lines, the proposed legal framework could include accountability mechanisms such as monitoring and reporting requirements, as well as the possibility for international courts or tribunals to adjudicate cases of femicide where national systems fail to provide justice.
The paramount importance of a new legally binding, international framework for combating femicide lies in its potential to create uniform standards, facilitate international cooperation, provide a basis for international monitoring and reporting, and enhance accountability. Binding international instruments carry greater weight and can compel states to adopt necessary legal reforms at the national level. They provide a solid basis for international monitoring and reporting, which can pressure states to comply with their international obligations.
A new framework would enhance the effectiveness of prevention measures by promoting educational campaigns, supporting women’s empowerment initiatives, and addressing the root causes of VAW. It would also strengthen prosecution efforts by standardizing legal definitions and procedures, thus reducing impunity for perpetrators. For victim protection, this framework would ensure that survivors and their families receive adequate support, including legal assistance and psychological care.
Furthermore, femicide requires urgent action because it has one of the gravest consequences of a plethora of possible crimes (i.e. the death of a person). This does not diminish the importance of other gender-based crimes against women. However, femicide is evidently the most extreme and damning one, and is very specific due to its gender-based motive. An examination of femicide as a gender-based crime proves that women are disproportionately impacted by gender-based killings, with these occurring not only in family or intimate-partner contexts but also in a wide variety of settings.
The commission of femicide symbolizes a failure not only for the victim’s community or her state, but for the whole international society and global population. This failure may be traced back to different causes, including actions or the inaction of the judicial system or institutions, or in other cases, lack of societal awareness about gender inequality. With these root causes at play, the commission of femicide reflects society’s understanding and response to gender-based violence by individuals, as well as mechanisms to ensure the perpetrator’s accountability.
Taking this argument further, it is useful to recall John Donne’s famous words “no man is an island.” The same can apply at the international relations level: no state is an island. All national legal systems are somehow entangled as they influence and transform each other while shaping international law. This allows us to understand femicide today as a global and international issue not simply because it is committed in all states but mostly because its roots (the structural gender inequality) are shared by all countries. Femicide is the product of a certain order of things that, by repeating itself at the national level, informs and structures gender relations globally around a hierarchy of power. This hierarchy then informs actions at both the national and individual levels. Femicide expresses the whole human population’s incapacity to have gender relations peacefully and equitably, to tolerate differences, and to accept the “other” as a person with dignity rather than an enemy or an object.
According to some scholars, national governments can implement truly effective policies against VAW only when this theme is expressly related to concrete gender-based crimes, such as femicide. A detailed criminal provision regulating femicide is likely to lead public institutions to undertake measures not only specifically concerning femicide but more broadly in the field of VAW, by framing the gender-related killings as a violation of women’s rights. This operation is fundamental to grasping the connections between all femicides worldwide. Therefore, a binding international legal framework would not only reinforce existing protections but also address the specific challenges posed by femicide, thereby fostering a more comprehensive and cohesive global response.
In Latin America, several countries, including Argentina and Mexico, have implemented national laws specifically addressing femicide, offering valuable insights for the development of an international legal framework. These femicide laws criminalize the gender-based killing of women and impose stricter penalties on perpetrators. They also include provisions for data collection, which has led to increasing awareness and reporting of femicide cases. For instance, Mexico toughened penalties for femicide after the Parliament’s approval of the 2007 Ley General de Acceso de las Mujeres a una Vida libre de Violencia. Currently, Article 325 of the federal criminal code foresees 40 to 60 years imprisonment for the commission of femicide, while aggravated homicide carries a sentence of 30 to 60 years imprisonment (“homicidio calificado,” Article 320).
However, the effectiveness of these national laws varies significantly across the region due to differences in enforcement, resources, and institutional practices. Despite the commendable legal provisions, the application of law often faces serious challenges in Latin America. Barriers to justice, such as a weak rule of law, high rates of corruption, judicial reluctance to VAW cases, and limited awareness of femicide as a structural issue, hinder progress. As criminal law scholar Corn highlights, judgments on femicide in this continent are not numerous, and predominantly concern intimate partner violence.
A notable example of femicide legislation can be found in the criminal code of Chile. For many years, Article 390 of the Chilean penal code categorized “femicidio” as a type of “parricidio” (parricide), which refers to the killing of a family member. As such, femicide requires a relationship between the victim and the perpetrator, either as spouses or as a de facto couple. Following recent reforms, however, the definition of femicide has been considerably expanded. The crime can now be punished with a more severe penalty than general homicide when committed under certain aggravating circumstances, such as abuse of power or within the context of domestic violence.
Currently, femicide differs from homicide in several key aspects, including the circumstances, context, and especially the gender-related motivation, which may include hatred towards women, discrimination, or a desire to control them. According to Article 390§1bis, femicide includes all gender-related killings by men (“el hombre que matare a una mujer en razón de su género”) and stipulates a penalty that could range from 15 years and one day to life imprisonment without parole (“con la pena de presidio mayor en su grado máximo a presidio perpetuo”). Under this definition, the perpetrator must be a man, and the victim must be a woman, thereby potentially excluding certain types of femicide, such as those involving members of the LGBTQI+ community. Additionally, femicide is no longer limited to intimate-partner violence. Still, it encompasses a broad range of relationships and circumstances under which a killing can be classified as femicide (e.g., the killing of a prostitute by a client).
These changes represent significant reforms to Chile’s femicide laws, making them more comprehensive and severe than before. However, as in many other Latin American countries, it remains difficult to gather broad and accurate data concerning the commission of femicide and the enforcement of related provisions. Notably, many femicides in Latin America go unreported or might not be classified as femicides in official records. This is often due to lack of awareness or recognition of the crime as femicide, reluctance from the victim or their families to report, a failure by state authorities to properly classify the crime, or the state’s weak rule of law—or a combination of all these factors.
Differently from Chile, other countries such as El Salvador, Guatemala, and Nicaragua codified femicide through not a penal code reform but an ordinary law. In these cases, femicide does not constitute a separate offense in the national criminal code, but is framed as a subcategory of homicide, modifying existing legislation. Specifically, Article 6 of the 2008 Guatemalan law against femicide (“Ley contra el Femicidio”) defines it through specific circumstantial elements: femicide is committed by anyone who, in the context of unequal relations of power between men and women, kills a woman because she is such (“en el marco de las relaciones desiguales de poder entre hombres y mujeres, diere muerte a una mujer por su condición de mujer.”).
This law is broad enough to encompass various circumstances under which femicide can occur, including both intimate and non-intimate relationships such as family, work, and friendship (“compañerismo”) relationships. As such, the Guatemalan law represented a model for other Latin American countries to expand the legal concept of femicide. In contrast, countries such as Nicaragua limit femicide to intimate partner killings (“las relaciones interpersonales de pareja”), specifying that the clause would apply to both marital and dating, current and previous relations. At the same time, however, the Guatemalan law requires the victim to be a woman, who is killed because of her gender, within the context of uneven power relations between men and women. Thus, the law’s scope of application can be interpreted as excluding femicides committed within the LGBTQI+ community.
In other Latin American legal systems, femicide is considered an aggravating circumstance of homicide, with no list of specific examples. This is the case in Argentina, where the only distinctive element of femicide is the context of “gender violence” in which the crime must occur, pursuant to the 2012 Ley N. 26.791. Like the Chilean provision, the Argentinian law explicitly requires the perpetrator to be a man, and the victim to be a woman, therefore excluding femicide in lesbian couples from its scope. Moreover, Argentinian law allows for a reduction of the penalty if the murderer acted in the throes of “emoción violenta” (violent emotion, Article 81of the Argentinian criminal code). Essentially, this provision could partly justify the murder of a woman by her husband who got under “emoción violenta” (e.g., after finding out she had a relationship with someone else).
By contrast, countries without specific femicide laws often rely on broader homicide statutes, which may not adequately address the gendered nature of these crimes. Unlike the Latin American context, the European legal framework presents significant fragmentation with respect to VAW, and no European country has explicitly codified femicide. The ECHR is the primary regional instrument for guaranteeing the protection of women’s rights. However, its provisions concerning only women’s rights are scarce, and primarily refer to the right to non-discrimination and the right to marry.
Strikingly, neither the Arab nor the Asian human rights system have any convention specifically addressing VAW or femicide. There is only a generic prohibition of non-discrimination both in the Arab Charter and in several constitutions of Asian countries, such as China and Japan. However, these systems do not expressly recognize VAW as a form of GBD, and both lack regional precedents on femicide. States are often reluctant to deal with this issue, as it is the most extreme manifestation of society’s failure to protect women’s lives.
An international convention or protocol on femicide could draw on these national experiences, incorporating best practices and addressing common challenges. By establishing clear, binding obligations for all state parties, such a framework would promote a more uniform and effective response to femicide globally. It would also facilitate international cooperation in areas such as extradition, information sharing, and joint investigations, which are crucial for tackling transnational aspects of femicide, such as human trafficking and organized crimes.
Conclusion
Considering the pervasiveness of femicide and its devastating impact on women’s rights, it is imperative for international law to explicitly recognize and address this crime. Addressing femicide through international law is key to upholding women’s right to life is upheld, and to promoting a world where women can live free from the constant threat of gender-based violence. This Essay has examined the existing international legal framework’s inadequacies in addressing femicide, emphasizing a critical need for a more cohesive and comprehensive approach.
Femicide represents not just an episodic, individual tragedy, but reflects broader structural gender inequalities and a systemic failure to adequately protect women. Despite the recognition of gender-based violence by instruments like CEDAW, significant gaps remain in protection and accountability. Current international frameworks lack specific provisions that recognize and criminalize femicide, leading to inconsistent definitions, protection regimes, and enforcement mechanisms across jurisdictions. At the regional level, initiatives such as the Belem do Para Convention in Latin America, and the Istanbul Convention in Europe have made strides in addressing various forms of VAW. Nonetheless, these conventions are limited in scope and are not universally binding. Moreover, the absence of coercive mechanisms and widespread reluctance among states to accept international responsibility undermine their effectiveness.
A comparative analysis reveals that some Latin American countries have enacted national laws specifically addressing femicide, offering valuable insights into potential international frameworks. However, the enforcement of these laws varies significantly, and many challenges remain due to institutional reluctance and lack of awareness. Conversely, other regions, including the Arab world, Asia, and Europe, lack specific legal provisions addressing femicide, highlighting the need for a universal approach.
The absence of any regulation of femicide in international law represents a failure of the international community because femicide is rooted in widespread misogynistic attitudes and structural inequalities that transcend national borders. By explicitly recognizing femicide as a distinct crime, international law (especially international criminal law) can more effectively highlight the gravity of this offense and the systemic issues that enable it.
A binding international legal framework would create uniform standards, facilitate international cooperation, and ensure accountability. Such a framework would enhance prevention measures, strengthen prosecution efforts, and ensure adequate support for survivors and their families. Given the grave consequences of femicide, addressing this issue is paramount in the global fight against gender-based violence. Ultimately, femicide is relevant in international law because, as Bunch chiefly underlined, gender-based violence is rooted in women’s common historical experience of oppression.
By establishing clear, binding obligations for all states, a binding international legal framework would promote a more uniform and effective response to femicide globally. It would signify a critical step toward achieving gender equality and safeguarding the lives of women worldwide.
* PhD candidate in international law at the Geneva Graduate Institute, Switzerland. I express my heartfelt gratitude to the editors of the Yale Journal of International Law. I am also grateful to Professor Emanuele Corn, Professor Maria Neus Torbisco Casals, and Giacomo Bruno for the fruitful discussions.