Sphere Theorems in Geometry
Differential Geometry
2009-07-01 v2 Analysis of PDEs
Abstract
In this paper, we give a survey of various sphere theorems in geometry. These include the topological sphere theorem of Berger and Klingenberg as well as the differentiable version obtained by the authors. These theorems employ a variety of methods, including geodesic and minimal surface techniques as well as Hamilton's Ricci flow. We also obtain here new results concerning complete manifolds with pinched curvature.
Cite
@article{arxiv.0904.2604,
title = {Sphere Theorems in Geometry},
author = {S. Brendle and R. M. Schoen},
journal= {arXiv preprint arXiv:0904.2604},
year = {2009}
}
Comments
Some typos corrected; to appear in Surveys in Differential Geometry