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Séminaire de Théorie spectrale et géométrie (Grenoble)
Table of contents for this volume | Previous article | Next articlePhilippe G. LeFloch
Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
Séminaire de Théorie spectrale et géométrie (Grenoble), 26 (2007-2008), p. 77-90, doi: 10.5802/tsg.261
Article PDF | Reviews MR 2654598 | Zbl 1191.53052
Class. Math.: 83C05, 53C50, 53C12
Keywords: Lorentzian geometry, injectivity radius, constant mean curvature foliation, harmonic coordinates
Résumé - Abstract
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.
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