Mathematical Sciences: Boundary Behavior of Holomorphic Functions of Several Complex Variables

小行星9322326 该奖项支持数学研究方面的理论边界行为的全纯函数的几个复杂的变量和相关问题。 工作的一个主要方向是关于全纯函数的边界值的可去除奇点，也就是说，当一个函数可以扩展到一个点和一个邻域作为全纯函数？ 这些点称为可移奇点。 一个相关的方向的工作集中在研究可移动集的全纯函数。 这些是一个全纯函数的自然边界值与连续函数的自然边界值一致的集合。 工作也将做域不一定有界的光滑流形，一个领域的几个复杂的变量，没有得到太多的关注。 最后，将继续研究柯西-黎曼函数的一维切片。 多复变出现在世纪初作为一个自然的产物研究的职能，一个复杂的变量。 很明显，这个理论与它的前身有很大的不同。 基本的几何是更难以掌握和函数理论有更多的亲和力与偏微分算子的一阶。 因此，它成长为一个混合学科结合了微分几何和微分方程的深刻特点。 许多基本结构是在过去三十年中确定的。 目前的研究仍然集中在理解这些基本的数学形式。 ***

9322326 Stout This award supports mathematical research on aspects of the theory of boundary behavior of holomorphic functions of several complex variables and related questions. One major direction of the work concerns removable singularities for the boundary values of holomorphic functions, that is, when can a function be extended to a point and a neighborhood as an holomorphic function? These points are called removable singularities. A related direction of the work focuses on the study of removable sets for holomorphic functions. These are sets where the natural boundary values of an holomorphic function agree with those of a continuous function. Work will also be done on domains which are not necessarily bounded by smooth manifolds, an area of several complex variables which has not received much attention to date. Finally, work will continue on the study of Cauchy-Riemann functions in terms of one-dimensional slices of their underlying domains. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms. ***