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Near-constant mean curvature solutions of the Einstein constraint equations with non-negative Yamabe metrics

Paul T Allen1, Adam Clausen2 and James Isenberg3

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We show that sets of conformal data on closed manifolds with the metric in the positive or zero Yamabe class, and with the gradient of the mean curvature function sufficiently small, are mapped to solutions of the vacuum Einstein constraint equations. This result extends previous work which required the conformal metric to be in the negative Yamabe class, and required the mean curvature function to be nonzero.


PACS

04.20.Jb Exact solutions

04.20.Ex Initial value problem, existence and uniqueness of solutions

02.40.Ky Riemannian geometries

MSC

58D17 Manifolds of metrics (esp. Riemannian)

83C15 Exact solutions

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 7 (7 April 2008)

Received 3 October 2007, in final form 12 February 2008

Published 18 March 2008



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