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February  2009, 23(1&2): 341-365. doi: 10.3934/dcds.2009.23.341

Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity

Philippe G. Lefloch 1, , Cristinel Mardare 2, and  Sorin Mardare 3,

1. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France
2. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Universite Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris
3. 

Institüt für Mathematik, Abt. Angewandte Mathematik, Universitüt Zürich, Winterthurerstrasse 190, 8057 Zürich, Swaziland

Received  November 2007 Revised  January 2008 Published  September 2008

Assuming minimal regularity assumptions on the data, we revisit the classical problem of findingisometric immersions into the Minkowski spacetime for hypersurfaces of a Lorentzian manifold.Our approach encompasses metrics having Sobolev regularity and Riemann curvature definedin the distributional sense, only.It applies to timelike, spacelike, or null hypersurfaces with arbitrary signature that possibly changesfrom point to point.
Keywords: Lorentzian manifold, Minkowski spacetime, isometric embedding, general hypersurface.
Mathematics Subject Classification: Primary: 53C50, 83C99; Secondary: 51B20, 57Q35, 14J70.
Citation: Philippe G. Lefloch, Cristinel Mardare, Sorin Mardare. Isometric immersions into the Minkowski spacetime for Lorentzian manifolds with limited regularity. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 341-365. doi: 10.3934/dcds.2009.23.341
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