caa a22 4500 44532015X CHVBK 20180317142701.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00023-010-0070-3 doi (NATIONALLICENCE)springer-10.1007/s00023-010-0070-3 Schwartz Fernando Department of Mathematics, University of Tennessee, Knoxville, USA aut A Volumetric Penrose Inequality for Conformally Flat Manifolds [Elektronische Daten] [Fernando Schwartz] We consider asymptotically flat Riemannian manifolds with non-negative scalar curvature that are conformal to $${\mathbb{R}^{n}{\setminus} \Omega, n\ge 3}$$, and so that their boundary is a minimal hypersurface. (Here, $${\Omega\subset \mathbb{R}^{n}}$$ is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is bounded below by $${\frac{1}{2}\left(V/\beta_{n}\right)^{(n-2)/n}}$$, where V is the Euclidean volume of Ω and β n is the volume of the Euclidean unit n-ball. This gives a partial proof to a conjecture of Bray and Iga (Commun. Anal. Geom. 10:999-1016, 2002). Surprisingly, we do not require the boundary to be outermost. Springer Basel AG, 2010 Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/1(2011-02-01), 67-76 1424-0637 12:1<67 2011 12 23 https://doi.org/10.1007/s00023-010-0070-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00023-010-0070-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Schwartz Fernando Department of Mathematics, University of Tennessee, Knoxville, USA aut NATIONALLICENCE 773 0- Annales Henri Poincaré SP Birkhäuser Verlag Basel 12/1(2011-02-01), 67-76 1424-0637 12:1<67 2011 12 23 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer