Injectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature

2008/12/14 by Philippe G. LeFloch, LeFloch, Philippe G.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0812.2671

openalex publication_date 2008/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the breakdown criterion in General Relativity

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