Rigidity of area-minimizing two-spheres in three-manifolds
Differential Geometry
2010-09-29 v2 Analysis of PDEs
Abstract
We give a sharp upper bound for the area of a minimal two-sphere in a three-manifold (M,g) with positive scalar curvature. If equality holds, we show that the universal cover of (M,g) is isometric to a cylinder.
Keywords
Cite
@article{arxiv.1002.2814,
title = {Rigidity of area-minimizing two-spheres in three-manifolds},
author = {H. Bray and S. Brendle and A. Neves},
journal= {arXiv preprint arXiv:1002.2814},
year = {2010}
}
Comments
Final version, to appear in Comm Anal Geom