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ISSN 1088-6826(e) ISSN 0002-9939(p)

The size of isoperimetric surfaces in -manifolds and a rigidity result for the upper hemisphere

Author(s): Michael Eichmair
Journal: Proc. Amer. Math. Soc. 137 (2009), 2733-2740.
MSC (2000): Primary 53C20
Posted: April 3, 2009
MathSciNet review: 2497486
Retrieve article in: PDF

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Abstract: We characterize the standard $\mathbb{S}^3$ as the closed Ricci-positive -manifold with scalar curvature at least having isoperimetric surfaces of largest area: $4\pi$ . As a corollary we answer in the affirmative an interesting special case of a conjecture of M. Min-Oo's on the scalar curvature rigidity of the upper hemisphere.

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