Local canonical foliations of Lorentzian manifolds with bounded curvature
نویسنده
چکیده
We consider pointed Lorentzian manifolds and construct “canonical” foliations by constant mean curvature (CMC) hypersurfaces. Our result assumes a uniform bound on the local sup-norm of the curvature of the manifold and on its local injectivity radius, only. The prescribed curvature problem under consideration is a nonlinear elliptic equation whose coefficients have limited regularity. The CMC foliation allows us to introduce CMC-harmonic coordinates, in which the coefficients of the Lorentzian metric have optimal regularity. Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique (CNRS), Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France. E-mail : [email protected] AMS Subject Classification. 83C05, 53C50, 53C12.
منابع مشابه
Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
We review recent work on the local geometry and optimal regularity of Lorentzian manifolds with bounded curvature. Our main results provide an estimate of the injectivity radius of an observer, and a local canonical foliations by CMC (Constant Mean Curvature) hypersurfaces, together with spatially harmonic coordinates. In contrast with earlier results based on a global bound for derivatives of ...
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