arXiv subjects
Publications and source records attributed to Yu. Burago.
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.}
This is the first paper of two ones. Here we prove that two compact Alexandrov surfaces of bounded integral curvature having no peak points are bi-Lipschitz equivalent if they are homeomorphic one to the other. Also conditions under that two ends having finite integral negative curvature are bi-Lipschitz equivalent are considered. In the second paper it is shown that a bi-Lipschitz constant can be estimated depending on several geometric characteristics.
This is a continuation of the joint paper with the same title by A.Belenkiy and Yu.Burago. It is proved here that two homeomorphic closed Alexandrov surfaces (of bounded integral curvature) are bi-Lipschitz with a constant depending only on upper bounds of their Euler number, diameters, negative integral curvatures, and two positive numbers e and l such that positive curvature of each embedded disk with perimeter not greater than l is not greater than π-e.