Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
Séminaire de théorie spectrale et géométrie, Tome 26 (2007-2008), pp. 77-90.

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 the curvature, our method requires only a sup-norm bound on the curvature near the given observer.

DOI : https://doi.org/10.5802/tsg.261
Classification : 83C05,  53C50,  53C12
Mots clés : Lorentzian geometry, injectivity radius, constant mean curvature foliation, harmonic coordinates
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     title = {Injectivity radius and optimal regularity of {Lorentzian} manifolds with bounded curvature},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {77--90},
     publisher = {Institut Fourier},
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     year = {2007-2008},
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     mrnumber = {2654598},
     zbl = {1191.53052},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/tsg.261/}
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LeFloch, Philippe G. Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature. Séminaire de théorie spectrale et géométrie, Tome 26 (2007-2008), pp. 77-90. doi : 10.5802/tsg.261. http://www.numdam.org/articles/10.5802/tsg.261/

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