Communications in Analysis and Geometry
Volume 18 (2010)
Rigidity of area-minimizing two-spheres in three-manifolds
Pages: 821 – 830
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.