Mathematical Sciences: "Manifolds with Ricci Curvature Bounds"

数学科学：“具有 Ricci 曲率界的流形”

• 批准号: 9504994
• 负责人: Tobias Colding
• 金额: $ 5.83万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-01 至 1998-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504994&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Manifolds; Ricci; Curvature

Colding 9504994 The proposed research deals with Riemannian manifolds with lower Ricci curvature bounds. In particular, rigidity and stability problems are proposed. For example, the investigator has previously shown that an n-manifold with a definite lower Ricci curvature bound which is sufficiently close to a fixed n-manifold has volume close to this manifold and is homeomorphic to it. A Riemannian manifold can be thought of as a curved space; the Ricci curvature of a Riemannian manifold gives a local measure of the curvature. The proposed research seeks to understand the Ricci curvature and its relationship to other metric quantities such as volume and the topology of the manifold.

本文研究的是具有下Ricci曲率界的黎曼流形。特别提出了刚性和稳定性问题。例如，研究者先前已经证明了一个具有确定的下里奇曲率界的n流形，它足够接近于一个固定的n流形，它的体积接近于这个流形并且是同纯的。黎曼流形可以被认为是一个弯曲空间；黎曼流形的里奇曲率给出了曲率的局部测度。提出的研究旨在了解里奇曲率及其与其他度量量的关系，如体积和流形的拓扑结构。