#### 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
Primary: 53Z05
Secondary: 83C99