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.
Keywords: Lorentzian geometry, injectivity radius, constant mean curvature foliation, harmonic coordinates
@article{TSG_2007-2008__26__77_0,
author = {Philippe G. LeFloch},
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},
address = {Grenoble},
volume = {26},
year = {2007-2008},
doi = {10.5802/tsg.261},
mrnumber = {2654598},
zbl = {1191.53052},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/tsg.261/}
}
TY - JOUR AU - Philippe G. LeFloch TI - Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature JO - Séminaire de théorie spectrale et géométrie PY - 2007-2008 SP - 77 EP - 90 VL - 26 PB - Institut Fourier PP - Grenoble UR - https://proceedings.centre-mersenne.org/articles/10.5802/tsg.261/ DO - 10.5802/tsg.261 LA - en ID - TSG_2007-2008__26__77_0 ER -
%0 Journal Article %A Philippe G. LeFloch %T Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature %J Séminaire de théorie spectrale et géométrie %D 2007-2008 %P 77-90 %V 26 %I Institut Fourier %C Grenoble %U https://proceedings.centre-mersenne.org/articles/10.5802/tsg.261/ %R 10.5802/tsg.261 %G en %F TSG_2007-2008__26__77_0
Philippe G. LeFloch. Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature. Séminaire de théorie spectrale et géométrie, Volume 26 (2007-2008), pp. 77-90. doi : 10.5802/tsg.261. https://proceedings.centre-mersenne.org/articles/10.5802/tsg.261/
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