Journal
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
Volume 34, Issue -, Pages 14-24Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.difgeo.2014.03.005
Keywords
Exponential map; Low regularity; (Totally) normal neighborhoods
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Funding
- FWF [P23714, P25326]
- OeAD project [WTZ CZ 15/2013]
- Austrian Science Fund (FWF) [P 23714, P 25326] Funding Source: researchfish
- Austrian Science Fund (FWF) [P25326, P23714] Funding Source: Austrian Science Fund (FWF)
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Given a pseudo-Riemannian metric of regularity C-1,C-1 on a smooth manifold, we prove that the corresponding exponential map is a bi-Lipschitz homeomorphism locally around any point. We also establish the existence of totally normal neighborhoods in an appropriate sense. The proofs are based on regularization, combined with methods from comparison geometry. (c) 2014 Elsevier B.V. All rights reserved.
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