In this first paper of two, it is proved that two compact Aleksandrov surfaces with bounded integral curvature and without peak points are bi-Lipschitzequivalent if they are homeomorphic. Also, conditions under which two tubes with finite negative part of integral curvature are bi-Lipschitz-equivalent are considered. In the second paper an estimate depending only on several geometric characteristics is found for a bi-Lipschitz constant.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Applied Mathematics