Remarks on Chebyshev coordinates

Details Remarks on Chebyshev coordinates Remarks on Chebyshev coordinates

2005-06-28

arxiv.org/abs/math/0506580v4

Mathematics

Differential Geometry

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Scientific paper

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 2\pi each, 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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