Static potentials and area minimizing hypersurfaces

Huang, Lan-Hsuan; Martin, Daniel; Miao, Pengzi

doi:10.1090/proc/13936

Static potentials and area minimizing hypersurfaces
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by Lan-Hsuan Huang, Daniel Martin and Pengzi Miao PDF

Proc. Amer. Math. Soc. 146 (2018), 2647-2661 Request permission

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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