The size of isoperimetric surfaces in 3-manifolds and a rigidity result for the upper hemisphere
Abstract
We characterize the standard S3 as the closed Ricci-positive 3-manifold with scalar curvature at least 6 having isoperimetric surfaces of largest area: 4π. As a corollary we answer in the affirmative an interesting special case of a conjecture of Min-Oo's on the scalar curvature rigidity of the upper hemisphere..
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