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.

冷水9504994拟议的研究涉及较低的RICCI曲率边界的Riemannian歧管。特别是，提出了刚性和稳定性问题。例如，研究者先前已经表明，具有确定的较低RICCI曲率结合的N-manifold足够接近固定的N-manifold的体积接近该歧管，并且与之同型。 可以将Riemannian歧管视为弯曲的空间。 riemannian歧管的RICCI曲率给出了曲率的局部度量。拟议的研究试图了解RICCI曲率及其与其他度量量的关系，例如数量和歧管的拓扑。