Extensions and fill-ins with non-negative scalar curvature

Jeffrey L. Jauregui, Pengzi Miao, Luen Fai Tam

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Abstract

Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown-York mass, to study a fill-in problem of realizing geometric data on a 2-sphere as the boundary of a compact 3-manifold of non-negative scalar curvature. We characterize the relationship between two borderline cases: one in which the Shi-Tam extension has zero total mass, and another in which fill-ins of non-negative scalar curvature fail to exist. Additionally, we prove a type of positive mass theorem in the latter case.

Original languageEnglish (US)
Article number195007
JournalClassical and Quantum Gravity
Volume30
Issue number19
DOIs
StatePublished - Oct 7 2013

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ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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