Vol. 298, No. 1, 2019

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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
Authors
Alexandre de Sousa
Instituto de Matemática
Universidade Federal de Alagoas
Maceió
Brazil
Frederico Girão
Departamento de Matemática
Universidade Federal do Ceará
Fortaleza
Brazil