Mathematical Sciences: Some Relations Between Partial Differential Equations and Geometry

数学科学：偏微分方程与几何之间的一些关系

• 批准号: 8902288
• 负责人: Jozef Dodziuk
• 金额: $ 6.35万
• 依托单位: CUNY Queens College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902288&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Relations; Between

The principal investigator will analyze various problems reflecting the interaction between partial differential equations and the geometry and topology of manifolds. Specifically, he will extend his existing work on L^2-cohomology and derive topological invariants for L^p-cohomology spaces. In addition, the problem of small eigenvalues of negatively curved manifolds will be investigated. L^p-cohomology has links with number theory, algebraic geometry, group representations, and combinatorial topology. The principal investigator will use his knowledge of the L^2 theory to solve two difficult but natural problems which arise from considering the more general L^p case.

主要研究人员将分析反映偏微分方程与流形的几何和拓扑之间的相互作用的各种问题。具体地说，他将推广他已有的关于L^2-上同调的工作，并得到L^p-上同调空间的拓扑不变量。此外，还将研究负曲线流形的小本征值问题。L的p-上同调与数论、代数几何、群表示和组合拓扑学有关。首席调查员将利用他对L^2理论的知识来解决两个困难但自然的问题，这两个问题是在考虑更一般的L^p案件时产生的。