Spaces with sectional and Ricci curvature bounds

具有截面和里奇曲率边界的空间

• 批准号: RGPIN-2017-06369
• 负责人: Kapovitch, Vitali
• 金额: $ 1.75万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=712215
• 关键词: Spaces; sectional; Ricci; curvature; bounds

Curvature of a space is its most important local geometric invariant. It describes how a space is shaped or curved locally from the point of view of an observer living inside that space. This proposal is mostly concerned with spaces with various lower curvature bounds. The notions of spaces with lower sectional and Ricci curvature bounds play an important role in a number of fields in mathematics and physics: general relativity, optimal transport, big data analysis and, of course, Riemannian geometry itself. I plan to study several problems concerning generalized spaces with lower sectional curvature bounds (Alexandrov spaces) and generalized spaces with lower Ricci curvature bounds (Restricted Curvature-Dimension condition). I am particularly interested in the interplay between these two conditions which as yet is not sufficiently understood.

空间的曲率是其最重要的局部几何不变量。它描述了从生活在该空间内的观察者的角度来看，空间是如何局部成形或弯曲的。