Vol. 306, No. 1, 2020

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A positive mass theorem for manifolds with boundary

Sven Hirsch and Pengzi Miao

Vol. 306 (2020), No. 1, 185–201
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
Authors
Sven Hirsch
Duke University
Durham, NC
United States
Pengzi Miao
Department of Mathematics
University of Miami
Coral Gables, FL
United States