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On mean curvature flow of spacelike hypersurfaces in asymptotically flat spacetimes

Part of: Spaces and manifolds of mappings Parabolic equations and systems General relativity

Published online by Cambridge University Press:  09 April 2009

Klaus Ecker
Klaus Ecker
Affiliation:
Department of Mathematics, The University of Melbourne, Parkville, Victoria 3052, Australia, email: ecker@mundoe.maths.mu.oz.au
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Abstract

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We prove a priori estimates for the gradient and curvature of spacelike hypersurfaces moving by mean curvature in a Lorentzian manifold. These estimates are obtained under much weaker conditions than have been previously assumed. We also use mean curvature flow in the construction of maximal slices in asymptotically flat spacetimes. An essential tool is a maximum principle for sub-solutions of a parabolic operator on complete Riemannian manifolds with time-dependent metric.

MSC classification

Secondary: 58D25: Equations in function spaces; evolution equations 83C99: None of the above, but in this section 35K55: Nonlinear parabolic equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 55 , Issue 1 , August 1993 , pp. 41 - 59
Copyright
Copyright © Australian Mathematical Society 1993

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