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arXiv · 2311.18570

Ambient Lipschitz geometry of normally embedded surface germs

Lev Birbrair·Davi Lopes Medeiros
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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 $\mathbb{R}^3$, 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.

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Lev Birbrair, Davi Lopes Medeiros. 2023-11-30. Ambient Lipschitz geometry of normally embedded surface germs. https://arxiv.org/abs/2311.18570

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