Ricci curvature, minimal surfaces and sphere theorems
dg-ga
2008-02-03 v1 Differential Geometry
Abstract
Using an analogue of Myers' theorem for minimal surfaces and three dimensional topology, we prove the diameter sphere theorem for Ricci curvature in dimension three and a corresponding eigenvalue pinching theorem. This settles these two open problems for closed 3 manifolds with positive Ricci curvature since they are both false in dimensions greater than three.
Keywords
Cite
@article{arxiv.dg-ga/9709002,
title = {Ricci curvature, minimal surfaces and sphere theorems},
author = {Ying Shen and Shunhui Zhu},
journal= {arXiv preprint arXiv:dg-ga/9709002},
year = {2008}
}
Comments
LaTex Form. To appear in J. Geom. Analysis