Vol. 294, No. 2, 2018

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ISSN: 0030-8730
A positive mass theorem and Penrose inequality for graphs with noncompact boundary

Ezequiel Barbosa and Adson Meira

Vol. 294 (2018), No. 2, 257–273
Abstract

We prove a version of the positive mass theorem for graph hypersurfaces with a noncompact boundary, in Euclidean space. We also prove a Penrose inequality for such hypersurfaces.

Keywords
graphical hypersurface, ADM mass, scalar curvature, rigidity, asymptotically flat
Mathematical Subject Classification 2010
Primary: 53C24, 83C99
Milestones
Received: 8 September 2016
Revised: 27 June 2017
Accepted: 5 December 2017
Published: 20 February 2018
Authors
Ezequiel Barbosa
Departamento de Matemática
Federal University of Minas Gerais
Belo Horizonte
Brazil
Adson Meira
Departamento de Matemática
Federal University of Minas Gerais
Belo Horizonte
Brazil