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A positive mass
theorem for manifolds with boundary
Sven Hirsch and Pengzi Miao |
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Vol. 306 (2020), No. 1, 185–201
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Abstract |
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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. |
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Keywords
positive mass theorem with boundary
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Mathematical Subject Classification 2010
Primary: 53Z05
Secondary: 83C99
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Milestones
Received: 19 March 2019
Revised: 6 July 2019
Accepted: 4 December 2019
Published: 14 June 2020
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Authors |
| Sven Hirsch | |
| Duke University Durham, NC United States |
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| Pengzi Miao | |
| Department of Mathematics University of Miami Coral Gables, FL United States |
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