The Gauss–Bonnet–Chern mass of higher-codimension graphs

Alexandre de Sousa and Frederico Girão

Vol. 298 (2019), No. 1, 201–216

DOI: 10.2140/pjm.2019.298.201

Abstract

We give an explicit formula for the Gauss–Bonnet–Chern mass of an asymptotically flat graph of arbitrary codimension and use it to prove the positive mass theorem and the Penrose inequality for graphs with flat normal bundle.

Keywords

Gauss–Bonnet–Chern mass, higher-codimension asymptotically flat graphs, positive mass theorem, Penrose inequality

Mathematical Subject Classification 2010

Primary: 53C40, 53C80, 83C99

Milestones

Received: 4 April 2017

Revised: 16 January 2018

Accepted: 13 May 2018

Published: 2 February 2019