Mathematical Sciences: Problems in Complex Analysis

Robert Gunning将继续他对函数和黎曼曲面的研究。目标是完整分析黎曼二阶函数在原点的偏导数之间的线性关系，扩展已知的关系，提供Korteweg-deVries和Kadomtsev- Petviashvili方程的显式解，以及这些关系在表征雅可比变量的肖特基问题中的作用的研究。Fornaess将研究复数变量空间中光滑有界域的泛函性质。我们的目标是在不同类型的域中获得某些微分方程的解的估计，扩展已知的强伪凸域的结果，并研究域的一致可扩展性的概念，这对于理解Bergman核函数在域边界的渐近行为至关重要。

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.