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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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A note on the Yamabe constant of an outermost minimal hypersurface
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by Fernando Schwartz PDF
Proc. Amer. Math. Soc. 138 (2010), 4103-4107 Request permission

Abstract:

Using an elementary argument we find an upper bound on the Yamabe constant of the outermost minimal hypersurface of an asymptotically flat manifold with nonnegative scalar curvature that satisfies the Riemannian Penrose Inequality. Provided the manifold satisfies the Riemannian Penrose Inequality with rigidity, we show that equality holds in the inequality if and only if the manifold is the Riemannian Schwarzschild manifold.
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Additional Information
  • Fernando Schwartz
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-0614
  • Email: fernando@math.utk.edu
  • Received by editor(s): November 5, 2009
  • Received by editor(s) in revised form: February 8, 2010
  • Published electronically: May 27, 2010
  • Additional Notes: This work was partially supported by The Leverhulme Trust
  • Communicated by: Richard A. Wentworth
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 4103-4107
  • MSC (2010): Primary 53C21, 83C99
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10445-8
  • MathSciNet review: 2679631