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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The size of isoperimetric surfaces in $3$-manifolds and a rigidity result for the upper hemisphere
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by Michael Eichmair PDF
Proc. Amer. Math. Soc. 137 (2009), 2733-2740 Request permission


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:
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2733-2740
  • MSC (2000): Primary 53C20
  • DOI:
  • MathSciNet review: 2497486