Mathematical Sciences: Research in Several Complex Variables and Application

数学科学：多复变量的研究及应用

• 批准号: 9622285
• 负责人: Laszlo Lempert
• 金额: $ 14.1万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-05-01 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9622285&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Several; Complex

9622285 Lempert The proposed research lies in the area of several complex variables. The investigator wishes to study how the property of embeddability of Cauchy-Riemann manifolds behaves when the Cauchy-Riemann structure is perturbed. In addition, the investigator plans to study various properties of infinite dimensional complex manifolds: the inhomogeneous Cauchy-Riemann equations in Hilbert spaces, the extension of the Newlander-Nirenberg theorem and the Oka principle are among the topics pursued. Spaces based on complex numbers arise in many natural settings. For example, polynomial equations in general can not be solved unless one works in a (finite dimensional) complex space. The proposed research deals with abstract complex spaces and infinite dimensional complex spaces.

9622285 Lempert 拟议的研究涉及几个复杂变量的领域。研究者希望研究当柯西-黎曼结构受到扰动时，柯西-黎曼流形的可嵌入性特性如何表现。此外，研究人员计划研究无限维复流形的各种性质：希尔伯特空间中的非齐次柯西-黎曼方程、纽兰德-尼伦堡定理的推广和奥卡原理都是所追求的主题。 基于复数的空间出现在许多自然环境中。例如，除非在（有限维）复空间中工作，否则一般无法求解多项式方程。所提出的研究涉及抽象复杂空间和无限维复杂空间。