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

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

2010-02-15

arxiv.org/abs/1002.2814v2

Mathematics

Differential Geometry

Final version, to appear in Comm Anal Geom

Scientific paper

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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