A class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature

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dc.creatorMaxwell, David
dc.date2008-04-05
dc.date.accessioned2026-07-07T09:30:42Z
dc.date.available2026-07-07T09:30:42Z
dc.descriptionWe give a sufficient condition, with no restrictions on the mean curvature, under which the conformal method can be used to generate solutions of the vacuum Einstein constraint equations on compact manifolds. The condition requires a so-called global supersolution but does not require a global subsolution. As a consequence, we construct a class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature, extending a recent result of Holst, Nagy, and Tsogtgerel [HNT07] which constructed similar solutions in the presence of matter. We give a second proof of this result showing that vacuum solutions can be obtained as a limit of [HNT07] non-vacuum solutions. Our principal existence theorem is of independent interest in the near-CMC case, where it simplifies previously known hypotheses required for existence.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/0804.0874
dc.identifierhttp://arxiv.org/abs/0804.0874
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158206
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectAnalysis of PDEs
dc.subjectDifferential Geometry
dc.titleA class of solutions of the vacuum Einstein constraint equations with freely specified mean curvature
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