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.

该项目涉及几个复杂变量领域出现的问题的数学研究。它涉及n维复合空间及其自动形态组中有界伪共元域的函数理论和几何特性。该研究的第一个目标是通过其边界的局部几何形状来识别具有非绘制自动形态群体的域。特别感兴趣的边界不完全光滑。该工作的第二个组成部分是扩展了有关在有界伪convex域上定义的内在不变指标的渐近行为的研究。该研究与自动形态的边界行为和自动形态群体的紧凑性有关。最后，将完成工作，通过具有非2型自动形态组的域之间的边界几何形状来识别有界的对称域。这些项目通过以下主题连接，即自动形态组的大小和有限域的边界几何形状被绑在一起。对几个复杂变量的研究最初是在本世纪初出现的，目的是检查经典函数理论的那些特性，这些理论推广到了几个变量。事实证明，大多数属性不会概括，而研究则转向了一些更有趣的几何和分析问题，这些问题仅在域名二维或更高时才出现。这个项目延续了这一传统。