Communications in Analysis and Geometry

Volume 18 (2010)

Number 4

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

Pages: 821 – 830



Hubert Bray (Department of Mathematics, Duke University, Durham, North Carolina)

Simon Brendle (Department of Mathematics, Stanford University)

Andre Neves (Imperial College London, United Kingdom)


We give a sharp upper bound for the area of a minimaltwo-sphere in a three-manifold $(M,g)$ with positive scalarcurvature. If equality holds, we show that the universalcover of $(M,g)$ is isometric to a cylinder.

Published 1 January 2010