Bi-Lipschitz equivalent Alexandrov surfaces, I

Details Bi-Lipschitz equivalent Alexandrov surfaces, I Bi-Lipschitz equivalent Alexandrov surfaces, I

2004-09-20

arxiv.org/abs/math/0409340v1

Mathematics

Differential Geometry

Scientific paper

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.

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