Rigidity of area-minimizing two-spheres in three-manifolds
classification
🧮 math.DG
math.AP
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areaarea-minimizingboundcovercurvaturecylinderequalitygive
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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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