The Nash modifications and the bi-Lipschitz equivalence

TL;DR

This paper explores the relationship between Nash modifications and bi-Lipschitz equivalence in the context of germs with isolated singularities, focusing on cases involving two germs and hypersurfaces.

Contribution

It establishes connections between Nash modifications and bi-Lipschitz equivalence for specific classes of singularities, advancing understanding in singularity theory.

Findings

Nash modifications relate to bi-Lipschitz equivalence in certain singularity cases

Results apply to pairs of germs and hypersurfaces with isolated singularities

Provides new insights into the structure of singularities under bi-Lipschitz transformations

Abstract

In this paper we investigate the relation betwen the Nash modification and the Bi-Lipschtiz equivalent germs in the cases of two germs and for a family of hypersurfaces with isolated singularities.