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.
Original language | English (US) |
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Pages (from-to) | 185-201 |
Number of pages | 17 |
Journal | Pacific Journal of Mathematics |
Volume | 306 |
Issue number | 1 |
DOIs | |
State | Published - Jun 2020 |
Keywords
- positive mass theorem with boundary
ASJC Scopus subject areas
- Mathematics(all)