Mathematical Sciences: "Manifolds with Ricci Curvature Bounds"

点击翻译按钮获取中文摘要

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.