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Contracting spacelike hypersurfaces by their inverse mean curvature

Part of: Global differential geometry General relativity

Published online by Cambridge University Press:  09 April 2009

Michael Holder
Michael Holder
Affiliation:
Mathematisches Institut Universität TübingenAuf der Morgenstelle 10 D-72076 TübingenGermany e-mail: [email protected]
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Abstract

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In this work we study the behaviour of compact, smooth, orientable, spacelike hypersurfaces without boundary, which are immersed in cosmological spacetimes and move under the inverse mean curvature flow. We prove longtime existence and regularity of a solution to the corresponding nonlinear parabolic system of partial differential equations.

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C50: Lorentz manifolds, manifolds with indefinite metrics 83C30: Asymptotic procedures (radiation, news functions, $scr H$-spaces, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 285 - 300
Copyright
Copyright © Australian Mathematical Society 2000

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