Mathematical Sciences: Problems in Complex Analysis

罗伯特·冈宁将继续他对θ函数的研究 黎曼曲面目标是完整的线性分析 黎曼二阶偏导数之间的关系 theta函数在原点，扩展了已知的关系， 提供Korteweg-deVries和Kadomtsev的显式解， Petviashvili方程，以及对 这些关系在肖特基问题的特征雅可比 品种 Fornaess将进行功能理论的研究 空间中光滑有界域的性质 复杂变量目标是获得 解的某些微分方程在各种类别的 领域，扩展了众所周知的结果， 伪凸域，并研究一致的概念， 域的可扩展性对于理解 的渐近行为的伯格曼核函数在 域的边界。

Robert Gunning will continue his research on theta functions and Riemann surfaces. The goal is the complete analysis of linear relations between partial derivatives of Riemannian second order theta functions at the origin, extending the known relations that provide explicit solutions of the Korteweg-deVries and Kadomtsev- Petviashvili equations, and the investigation of the role of these relations in the Schottky problem of characterizing Jacobi varieties. Fornaess will carry out research on function-theoretic properties of smoothly bounded domains in the space of several complex variables. The goals are to obtain estimates for solutions of certain differential equations in various classes of domains, extending results that are known for strongly pseudoconvex domains, and to study a notion of uniform extendability of domains that seems critical to the understanding of the asymptotic behaviour of the Bergman kernel function at the boundary of a domain.