Bi-Lipschitz equivalent Alexandrov surfaces, I
Differential Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0409340,
title = {Bi-Lipschitz equivalent Alexandrov surfaces, I},
author = {A. Belenkiy and Yu. Burago},
journal= {arXiv preprint arXiv:math/0409340},
year = {2007}
}