A positive mass theorem and Penrose inequality for graphs with noncompact boundary

Ezequiel Barbosa and Adson Meira

Vol. 294 (2018), No. 2, 257–273

DOI: 10.2140/pjm.2018.294.257

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