A note on the Yamabe constant of an outermost minimal hypersurface

• Autores: Fernando Schwartz
• Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 11, 2010, págs. 4103-4107
• Idioma: inglés
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• Resumen

  • 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.