Riemann maps in almost complex manifolds

We prove the existence of stationary discs in the ball for small almost complex deformations of the standard structure. We define a local analogue of the Riemann map and establish its main properties. These constructions are applied to study the local geometry of almost complex manifolds and their morphisms.Comment: 2003.6.1

Fefferman's mapping theorem on almost complex manifolds

We give a necessary and sufficient condition for the smooth extension of a diffeomorphism between smooth strictly pseudoconvex domains in four real dimensional almost complex manifolds. The proof is mainly based on a reflection principle for pseudoholomorphic discs, on precise estimates of the Kobayashi-Royden infinitesimal pseudometric and on the scaling method in almost complex manifolds

Neither Dyad Nor Triad: Children\u27s Relationship Interests Within Kinship Caregiving Families

Utilizing a research design lens as a platform for exploring children\u27s relationship rights, this Essay examines first, the limitations of a rights-based framework and second, insufficient participation by children in decision-making regarding their access to and interest in relationships with significant others. This Essay posits that neither the dyadic rights-based framework in domestic relations nor the, ostensibly, triadic one in child welfare serve the interests of children, since children\u27s rights are invariably subordinated to those of adults and the state. In place of a rights-based approach, this Essay endorses an interests-based model more attuned to the holistic aim of child well-being. Acknowledging that even if an interest-based approach were to grow in favor this Essay highlights the limitations of its implementation since the proverbial best interests of the child remains too attenuated as a critical decision-making factor due to currently limited mechanisms of children\u27s participation. This Essay argues that these limitations are particularly harmful to the development of a meaningful discourse on children\u27s relationship rights

Corruption, Investment and Economic Growth: Theory and International Evidence

This paper analyzes the real effects of corruption on a firm’s production function. Using an augmented-Solow Growth model, with multifactor productivity as a function of corruption, a closed-form solution is derived for real GDP per capita, economic growth and physical capital per capita, at steady-state. With the a priori assumption of a negative relationship between corruption and multifactor productivity, it is shown that corruption negates a society’s standard of living, economic growth and investment level. OLS results of the closed-form solutions not only support this theoretical finding for a full cross-section of countries, but they also reveal that corruption may have a positive concave effect on economic variables for the OECD sample. Nonlinear least squares estimates of the elasticities of physical and human capital, with the inclusion of the corruption index, confirm that the productivity of inputs is impacted. &nbsp

Valuing All Identities Beyond the Schoolhouse Gate: The Case for Inclusivity as a Civic Virtue in K-12

Increasing social and political polarization in our society continues to exact a heavy toll marked by, among other social ills, a rise in uncivility, an increase in reported hate crimes, and a more pronounced overall climate of intolerance—for viewpoints, causes, and identities alike. Intolerance, either a cause or a consequence of our fraying networks of social engagement, is rampant, hindering our ability to live up to our de facto national motto, “E Pluribus Unum,” or “Out of Many, One” and prompting calls for how best to build a cohesive civil society. Within the public school—an institution conceived primarily for the purpose of inculcating civic virtues thought necessary to foster solidarity in a pluralistic society—the intolerance has contributed to increased bias-based bullying, particularly toward transgender and gender diverse students. The devastating impacts of intolerance and exclusion on transgender and gender-diverse students include disproportionate rates of psychological distress, physical ailments, increased risk of homelessness, and other negative outcomes. As schools ponder how best to meet their needs and create safe and supportive learning environments, some parents have attempted to assert exclusive authority in this domain, challenging practices such as the adoption of gender-complex and LGBTQ-inclusive curricula as well as gender-affirming policies and practices. Parents allege that attempts by schools to accommodate transgender and gender diverse students infringe on their parental rights and the privacy rights of their cisgender children. While some schools have yielded to parental objections, others have resisted. This Article presents a compelling approach for schools both to address the challenges posed by objecting parents and to carry out their original mission of inculcating an appreciation for democratic norms—namely, civility, tolerance, and equality— through the adoption of gender complex and LGBTQ-inclusive curricula. Relying on both long-standing limitations on parents’ ability to exercise curricular control and research on the benefits of inclusive and comprehensive curricula, this Article makes the case that the educational purposes served by gender complex and LGBTQ-inclusive curricula more than justify any alleged burden on parents’ free exercise of religion as protected by the First Amendment or any alleged infringement upon parents’ substantive due process rights as protected by the Fourteenth Amendment. It posits that although both parents and the state share responsibility for shaping our youngest citizens, parental interests should be subordinate to the interests of the state in promoting proteophilic competence—an appreciation for diversity—through public education. This critical educational mission holds the promise of reaching beyond the scope of gender to include the inculcation of civic virtues essential to the health of an increasingly demographically diverse nation: Respect for “other-ness” and the development of skills needed for effective democratic self-governance