Static potentials and area minimizing hypersurfaces
Differential Geometry
2017-10-03 v2
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.
Cite
@article{arxiv.1706.03734,
title = {Static potentials and area minimizing hypersurfaces},
author = {Lan-Hsuan Huang and Daniel Martin and Pengzi Miao},
journal= {arXiv preprint arXiv:1706.03734},
year = {2017}
}
Comments
Several minor changes throughout the article for a better presentation. Accepted by Proceedings of the AMS