Proceedings of the American Mathematical Society

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
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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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Michael Eichmair
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Email: eichmair@math.mit.edu

DOI: 10.1090/S0002-9939-09-09789-5
PII: S 0002-9939(09)09789-5
Received by editor(s): December 3, 2007,
Received by editor(s) in revised form: September 17, 2008
Posted: April 3, 2009
Communicated by: Richard A. Wentworth
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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