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.References
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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