@article{e165d830742e4befb58dff0ffcbba82b,
title = "Static potentials and area minimizing hypersurfaces",
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{\textquoteright}s quasi-local mass are obtained.",
author = "Huang, {Lan Hsuan} and Daniel Martin and Pengzi Miao",
note = "Funding Information: Received by the editors June 21, 2017, and, in revised form, June 24, 2017, August 14, 2017, and August 26, 2017. 2010 Mathematics Subject Classification. Primary 53C21. The first two authors were partially supported by the NSF through grant DMS 1452477. The third author was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105. Funding Information: The first two authors were partially supported by the NSF through grant DMS 1452477. The third author was partially supported by Simons Foundation Collaboration Grant for Mathematicians #281105. Publisher Copyright: {\textcopyright} 2018 Amerian Mathematial Soiety.",
year = "2018",
doi = "10.1090/proc/13936",
language = "English (US)",
volume = "146",
pages = "2647--2661",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "6",
}