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

Author:
Michael Eichmair

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2733-2740

MSC (2000):
Primary 53C20

DOI:
https://doi.org/10.1090/S0002-9939-09-09789-5

Published electronically:
April 3, 2009

MathSciNet review:
2497486

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Abstract: We characterize the standard as the closed Ricci-positive -manifold with scalar curvature at least having isoperimetric surfaces of largest area: . 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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Additional Information

**Michael Eichmair**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307

Email:
eichmair@math.mit.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-09789-5

Received by editor(s):
December 3, 2007

Received by editor(s) in revised form:
September 17, 2008

Published electronically:
April 3, 2009

Communicated by:
Richard A. Wentworth

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.