Bray, H; Brendle, S; Neves, A, Rigidity of area-minimizing two-spheres in three-manifolds,
Communications in Analysis and Geometry, vol. 18 no. 4
(2010),
pp. 821-830 [arXiv:1002.2814], [doi] .
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.