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The size of isoperimetric surfaces in $ 3$-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
Published electronically: April 3, 2009
MathSciNet review: 2497486
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Abstract: We characterize the standard $ \mathbb{S}^3$ as the closed Ricci-positive $ 3$-manifold with scalar curvature at least $ 6$ 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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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.