Mathematical Sciences: Geometric Function Theory in Several Complex Variables

该项目所涵盖的一般研究领域 涉及多复变量和偏微分方程的理论， 微分方程 一个特别令人关注的问题是， Cauchy-Riemann延拓唯一性定理 流形 基本上这些研究涉及的问题是， 或者不是一个多变量的全纯函数， 沿着域的各种子流形的沿着常数，而不被 到处都是常数。 工作的第二个方面将侧重于 全纯映射下保持集的性质 在不同维度的空间之间。 的大部分 在一维情况下，直观上显而易见的是， 在更高维度的设置中为false。

The general area of research encompassed by this project relates to the theory of several complex variables and partial differential equations. One question of particular concern is that of the uniqueness of continuation in Cauchy-Riemann manifolds. Basically these studies involve questions of whether or not a holomorphic function of several variables can be constant along various submanifolds of a domain without being constant everywhere. A second aspect of the work will focus on the properties of sets preserved under holomorphic mappings between spaces of different dimensions. Much of what is intuitively obvious in the one dimensional case turns out to be false in higher dimensional settings.