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Remarks on Chebyshev coordinates. (English. Russian original) Zbl 1151.53349

J. Math. Sci., New York 140, No. 4, 497-501 (2007); translation from Zap. Nauchn. Semin. POMI 329, 5-13 (2005).
Summary: Some results on the existence of global Chebyshev coordinates on a Riemannian two-manifold or, more generally, on an Aleksandrov surface \(M\) are proved. For instance, if the positive and the negative part of the integral curvature of \(M\) are less than \(2\pi\), then there exist global Chebyshev coordinates on \(M\). Such coordinates help one to construct bi-Lipschitz maps between surfaces.

MSC:

53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
53B21 Methods of local Riemannian geometry
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References:

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