Ambient Lipschitz geometry of normally embedded surface germs
Metric Geometry
2024-12-02 v2 Algebraic Geometry
Abstract
We study the ambient Lipschitz geometry of semialgebraic surfaces. It was discovered in \cite{BBG} that ambient Lipschitz Geometry is different from the outer Lipschtz geometry. We show that two surface germs in , Lipschitz normally embedded and with isolated singularity, are ambient bi-Lipschitz equivalent if, and only if, they are outer bi-Lipschitz equivalent and ambient topologically equivalent.
Keywords
Cite
@article{arxiv.2311.18570,
title = {Ambient Lipschitz geometry of normally embedded surface germs},
author = {Lev Birbrair and Davi Lopes Medeiros},
journal= {arXiv preprint arXiv:2311.18570},
year = {2024}
}
Comments
64 pages, 38 figures. In the second version, several typos were corrected and some proofs were optimized. We also added a section devoted to prove the main result for several connected components with isolated singularity, showing also a counterexample with non-isolated singularity