Mathematical Sciences: Problems in Complex Analysis

Robert Gunning将继续他对theta函数和Riemann曲面的研究。其目的是完整地分析黎曼二阶函数在原点的偏导数之间的线性关系，推广已知的提供Korteweg-DeVries和Kadomtsev-Petviashvili方程显式解的关系，并研究这些关系在刻画Jacobi簇的肖特基问题中的作用。福奈斯将在多个复变量空间中对光滑有界域的函数论性质进行研究。其目的是得到不同类型区域上某些微分方程解的估计，推广了已知的关于强伪凸域的结果，并研究区域的一致可拓展性的概念，这似乎对于理解区域边界上的Bergman核函数的渐近行为是至关重要的。

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.