Rigidity of area-minimizing two-spheres in three-manifolds

2010/02/15 by Bray, H., Brendle, S., Neves, A. · 8 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1002.2814

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.

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