Variational Effect of Boundary Mean Curvature on ADM Mass in General Relativity

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dc.creatorMiao, Pengzi
dc.date2003-09-18
dc.date.accessioned2026-07-07T04:30:34Z
dc.date.available2026-07-07T04:30:34Z
dc.descriptionWe extend the idea and techniques in \cite{Miao} to study variational effect of the boundary geometry on the ADM mass of an asymptotically flat manifold. We show that, for a Lipschitz asymptotically flat metric extension of a bounded Riemannian domain with quasi-convex boundary, if the boundary mean curvature of the extension is dominated by but not identically equal to the one determined by the given domain, we can decrease its ADM mass while raising its boundary mean curvature. Thus our analysis implies that, for a domain with quasi-convex boundary, the geometric boundary condition holds in Bartnik's minimal mass extension conjecture \cite{Bartnik_energy}.
dc.description13 pages. This paper is closely related to math-ph/0212025
dc.identifierhttps://arxiv.org/abs/math-ph/0309045
dc.identifierhttp://arxiv.org/abs/math-ph/0309045
dc.identifierMathematical Physics Research on the Leading Edge, Nova Sci. Publ. NY, 2004, 145--171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57505
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.titleVariational Effect of Boundary Mean Curvature on ADM Mass in General Relativity
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