Static potentials and area minimizing hypersurfaces

Lan Hsuan Huang, Daniel Martin, Pengzi Miao

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2647-2661
Number of pages15
JournalProceedings of the American Mathematical Society
Volume146
Issue number6
DOIs
StatePublished - Jan 1 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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