Curvature, sphere theorems, and the Ricci flow
Differential Geometry
2010-06-01 v2 Analysis of PDEs
Geometric Topology
Metric Geometry
Abstract
This is a survey paper focusing on the interplay between the curvature and topology of a Riemannian manifold. The first part of the paper provides a background discussion, aimed at non-experts, of Hopf's pinching problem and the Sphere Theorem. In the second part, we sketch the proof of the Differentiable Sphere Theorem, and discuss various related results. These results employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton's Ricci flow.
Keywords
Cite
@article{arxiv.1001.2278,
title = {Curvature, sphere theorems, and the Ricci flow},
author = {S. Brendle and R. M. Schoen},
journal= {arXiv preprint arXiv:1001.2278},
year = {2010}
}
Comments
This is an invited contribution for the Bulletin of the AMS