Ambient Lipschitz geometry of normally embedded surface germs
Abstract
We study the ambient Lipschitz geometry of semialgebraic surfaces. It was discovered in BBG that ambient Lipschitz Geometry is different from the outer Lipschtz geometry. We show that two surface germs in R3, 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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