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تسجيل مستخدم جديدInjectivity radius and optimal regularity of Lorentzian manifolds with bounded curvature
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تأليف
Philippe G. LeFloch
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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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