Mathematical Sciences: Singular Solutions of Elliptic Equations and Analysis on Non-Compact Manifolds

数学科学：椭圆方程的奇异解和非紧流形分析

• 批准号: 9222491
• 负责人: Mikhail Shubin
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-02-01 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9222491&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Singular; Solutions; Elliptic

The research concerns singularities of solutions of partial differential equations on manifolds. Implicit in this work are heat-equation analysis and topology of singular spaces. From this one can study Hilbert/Fredhom complexes and related cohomology theories. This leads to certain generalizations of the classical Riemann-Roch theorem.

本文研究了偏微分方程解的奇性 流形上的微分方程在这项工作中隐含的是 热方程分析和奇异空间拓扑学。从这个 我们可以研究希尔伯特/弗雷德霍姆复形和相关的上同调 理论这导致了经典的某些概括 黎曼-罗克定理