A POSITIVE MASS THEOREM FOR MANIFOLDS WITH BOUNDARY

Sven Hirsch, Pengzi Miao

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green’s function. The theorem also holds if the conformal Green’s function is replaced by the standard Green’s function for the Laplacian operator. As an application, we obtain an inequality relating the mass and harmonic functions that generalizes H. Bray’s mass-capacity inequality in his proof of the Riemannian Penrose conjecture.

Original languageEnglish (US)
Pages (from-to)185-201
Number of pages17
JournalPacific Journal of Mathematics
Volume306
Issue number1
DOIs
StatePublished - Jun 2020

Keywords

  • positive mass theorem with boundary

ASJC Scopus subject areas

  • Mathematics(all)

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