On a Localized Riemannian Penrose Inequality

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18 Scopus citations


Let Ω be a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary ∂Ω is the disjoint union of two pieces: ΣH and ΣO, where ΣH consists of the unique closed minimal surfaces in Ω and ΣO is metrically a round sphere. We obtain an inequality relating the area of ΣH to the area and the total mean curvature of ΣO. Such an Ω may be thought of as a region, surrounding the outermost apparent horizons of black holes, in a time-symmetric slice of a space-time in the context of general relativity. The inequality we establish has close ties with the Riemannian Penrose Inequality, proved by Huisken and Ilmanen [9] and by Bray [5].

Original languageEnglish (US)
Pages (from-to)271-284
Number of pages14
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Aug 2009
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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