Mathematical Sciences: Geometric Invariants, Pseudodifferential Operators and Several Complex Variables

数学科学：几何不变量、伪微分算子和多个复变量

• 批准号: 9001957
• 负责人: Charles Epstein
• 金额: $ 9.24万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001957&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Invariants; Pseudodifferential

The principal investigator will study global invariants on strictly pseudoconvex manifolds that arise as renormalized Chern classes for complete Kaehler metrics. He will continue his study of pseudodifferential operator calculi adapted to the study of degenerate operators similiar to the Bergman-Laplace operator. A goal will be to obtain index formulae relating the renormalized Chern numbers to "analytic" indices for degenerate elliptic complexes. And he will continue an investigation of the problem of embedding three dimensional CR-manifolds. For many years mathematicians have studied the behavior of certain differential operators on hypersurfaces which extend off to infinity. This study has its origins in the calculus of Newton. In this project the principal investigator will analyze operators which have large variations over very large domains "near" infinity. In the past, only progress on operators which have small local variations was made.

主要研究者将研究全局不变量 严格伪凸流形，作为重正化陈 完整Kaehler度量的类。 他将继续他的学习 的伪微分算子演算适应的研究 退化算子类似于Bergman-Laplace算子。 一 目标将是获得指数公式有关的重整化 退化椭圆方程的“解析”指标的Chern数 配合物 他将继续调查这个问题 嵌入三维CR流形的方法 多年来，数学家们一直在研究 超曲面上的某些微分算子 到无穷远 这项研究起源于微积分， 牛顿 在这个项目中，首席研究员将分析 在非常大的域上有很大变化的算子 “接近”无穷大。 在过去，只有在运营商方面取得进展， 有小的局部变化。