A positive mass theorem for manifolds with boundary

Sven Hirsch and Pengzi Miao

Vol. 306 (2020), No. 1, 185–201

DOI: 10.2140/pjm.2020.306.185

Abstract

We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green’s function. The theorem also holds if the conformal Green’s function is replaced by the standard Green’s function for the Laplacian operator. As an application, we obtain an inequality relating the mass and harmonic functions that generalizes H. Bray’s mass-capacity inequality in his proof of the Riemannian Penrose conjecture.

Keywords

positive mass theorem with boundary

Mathematical Subject Classification 2010

Primary: 53Z05

Secondary: 83C99

Milestones

Received: 19 March 2019

Revised: 6 July 2019

Accepted: 4 December 2019

Published: 14 June 2020