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

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  • 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.
    Mathematics Subject Classification: Primary: 53C50, 83C99; Secondary: 51B20, 57Q35, 14J70.

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