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Remarks on Chebyshev coordinates

Yu. Burago·S. Ivanov·S. Malev
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Abstract

Some results on existence of global Chebyshev coordinates on a Riemannian manifold or, more generally, on Aleksandrov surface are proved. For instance, if the positive and the negative parts of integral curvature of a Riemannian manifold M are less than 2πeach, then there exist global Chebyshev coordinates on M. These conditions are optimal. Such coordinates help to get bi-Lipschitz maps between surfaces.}

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Yu. Burago, S. Ivanov, S. Malev. 2005-12-11. Remarks on Chebyshev coordinates. https://arxiv.org/abs/math/0506580

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