Static potentials and area minimizing hypersurfaces
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- by Lan-Hsuan Huang, Daniel Martin and Pengzi Miao PDF
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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.References
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Additional Information
- Lan-Hsuan Huang
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 861470
- 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
- MR Author ID: 715810
- Email: pengzim@math.miami.edu
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 2647-2661
- MSC (2010): Primary 53C21
- DOI: https://doi.org/10.1090/proc/13936
- MathSciNet review: 3778165