Mathematical Sciences: Geometric Function Theory in Several Complex Variables

数学科学：多复变数的几何函数论

• 批准号: 9025026
• 负责人: Jean-Pierre Rosay
• 金额: $ 5.8万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-05-15 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9025026&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Function; Theory

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.

该项目涵盖的一般研究领域涉及多个复变量和偏微分方程的理论。 特别值得关注的一个问题是柯西-黎曼流形中连续性的唯一性。 基本上，这些研究涉及的问题是多个变量的全纯函数是否可以沿着域的各个子流形保持恒定，而不是处处恒定。 这项工作的第二个方面将重点关注不同维度空间之间的全纯映射下保留的集合的属性。 一维情况下直观上显而易见的大部分内容在更高维度的设置中却​​被证明是错误的。