Local canonical foliations of Lorentzian manifolds with bounded curvature

Philippe G. LeFloch

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arXiv · 0812.3960

Local canonical foliations of Lorentzian manifolds with bounded curvature

Philippe G. LeFloch

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Abstract

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.

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Philippe G. LeFloch. 2008-12-20. Local canonical foliations of Lorentzian manifolds with bounded curvature. https://arxiv.org/abs/0812.3960

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