A note on the Yamabe constant of an outermost minimal hypersurface

Author:
Fernando Schwartz

Journal:
Proc. Amer. Math. Soc. **138** (2010), 4103-4107

MSC (2010):
Primary 53C21, 83C99

Published electronically:
May 27, 2010

MathSciNet review:
2679631

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Abstract | References | Similar Articles | Additional Information

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

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10445-8

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

Article copyright:
© Copyright 2010
American Mathematical Society

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