Mathematical Sciences: Geometric Function Theory in Several Complex Variables

这个项目所涵盖的一般研究领域涉及几个复变量理论和偏微分方程式。一个特别值得关注的问题是柯西-黎曼流形中连续的唯一性问题。基本上，这些研究涉及多个变量的全纯函数是否可以沿区域的各个子流形恒定而不是处处恒定的问题。这项工作的第二个方面将集中在不同维空间之间的全纯映射下保持的集的性质。在一维的情况下，许多直观上显而易见的东西在更高维的环境中被证明是错误的。

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.