Mathematical Sciences: Domains of Holomorphy and Their Automorphisms

数学科学：全纯域及其自同构

基本信息

批准号：
9201019
负责人：
Kang-Tae Kim
金额：
$ 3.5万
依托单位：
Brown University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1992
资助国家：
美国
起止时间：
1992-08-15 至 1995-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201019&HistoricalAwards=false
关键词：
Mathematical Sciences Domains Holomorphy Their

项目摘要

This project concerns mathematical research on problems arising in the area of several complex variables. It involves the function-theoretic and geometric properties of bounded pseudoconvex domains in n-dimensional complex space and their automorphism groups. The first goal of the research is to identify domains with noncompact automorphism groups by the local geometry of their boundaries. Particular interest is placed on boundaries which are not entirely smooth. The second component of the work is the extension of studies on the asymptotic behavior of the intrinsic invariant metrics defined on the bounded pseudoconvex domains. The research relates the boundary behavior of the automorphisms and the compactness of the automorphism groups. Finally, work will be done identifying the bounded symmetric domains by their boundary geometry among domains with noncompact automorphism groups. The projects are connected by the theme that the size of the automorphism groups and the boundary geometry of bounded domains are tied together. The study of several complex variables arose at the beginning of the century initially to examine those properties of classical function theory which generalize to several variables. It turned out that most properties do not generalize and research turned instead toward some of the more intriguing geometric and analytic questions which arise only when the domains are of dimension two or greater. This project continues that tradition.

该项目涉及对几个复杂变量领域中出现的问题的数学研究。它涉及n维复空间中有界伪凸域及其自同构群的函数论和几何性质。该研究的第一个目标是通过边界的局部几何形状来识别具有非紧自同构群的域。人们对不完全平滑的边界特别感兴趣。这项工作的第二个组成部分是对有界伪凸域上定义的内在不变度量的渐近行为的研究的扩展。研究将自同构的边界行为与自同构群的紧性联系起来。最后，将通过具有非紧自同构群的域之间的边界几何形状来识别有界对称域。这些项目的主题是自同构群的大小和有界域的边界几何联系在一起。对多个复变量的研究兴起于本世纪初，最初是为了检验经典函数理论推广到多个变量的性质。事实证明，大多数性质都不能概括，研究转向一些更有趣的几何和分析问题，这些问题仅在域为二维或更大维度时才会出现。这个项目延续了这一传统。