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Given a pseudo-Riemannian metric of regularity $C^{1,1}$ on a smooth manifold, we prove that the corresponding exponential map is a bi-Lipschitz homeomorphism locally around any point.
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Cheeger, J., Gromov, M., Taylor, M., Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Diff. Geom
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Harris, S. G., A Triangle Comparison Theorem for Lorentz Manifolds, Indiana Univ. Math. J
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do Carmo, M. P., Riemannian geometry
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Chruściel, P. T., Elements of causality theory, arXiv:1110.6706
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Grosser, M., Kunzinger, M., Oberguggenberger, M., Steinbauer, R., Geometric Theory of Generalized Functions
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Chen, B.-L., LeFloch, P., Injectivity Radius of Lorentzian Manifolds, Comm. Math. Phys
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Jost, J., Riemannian Geometry and Geometric Analysis
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