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Static potentials and area minimizing hypersurfaces


Authors: Lan-Hsuan Huang, Daniel Martin and Pengzi Miao
Journal: Proc. Amer. Math. Soc. 146 (2018), 2647-2661
MSC (2010): Primary 53C21
DOI: https://doi.org/10.1090/proc/13936
Published electronically: January 26, 2018
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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.


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Lan-Hsuan Huang
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: lan-hsuan.huang@uconn.edu

Daniel Martin
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: daniel.martin@uconn.edu

Pengzi Miao
Affiliation: Department of Mathematics, University of Miami, Coral Gables, Florida 33146
Email: pengzim@math.miami.edu

DOI: https://doi.org/10.1090/proc/13936
Received by editor(s): June 21, 2017
Received by editor(s) in revised form: June 24, 2017, August 14, 2017, and August 26, 2017
Published electronically: January 26, 2018
Additional Notes: 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.
Communicated by: Guofang Wei
Article copyright: © Copyright 2018 American Mathematical Society

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