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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: 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

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.

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