Abstract
We show that if an asymptotically flat manifold with horizon boundary admits a global static potential, then the static potential must be zero on the boundary. We also show that if an asymptotically flat manifold with horizon boundary admits an unbounded static potential in the exterior region, then the manifold must contain a complete non-compact area minimizing hypersurface. Some results related to the Riemannian positive mass theorem, and Bartnik’s quasi-local mass are obtained.
Original language | English (US) |
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Pages (from-to) | 2647-2661 |
Number of pages | 15 |
Journal | Proceedings of the American Mathematical Society |
Volume | 146 |
Issue number | 6 |
DOIs | |
State | Published - 2018 |
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics