Bi-Lipschitz A-equivalence of K-equivalent map germs

TL;DR

This paper establishes conditions under which K-equivalent map germs are also bi-Lipschitz A-equivalent, extending classical smooth equivalence results to the Lipschitz setting and providing a Lipschitz analogue of the Fukuda-Fukuda theorem.

Contribution

It introduces Lipschitz conditions that ensure bi-Lipschitz A-equivalence for K-equivalent map germs, extending smooth equivalence theories to Lipschitz contexts.

Findings

Provided two sufficient Lipschitz conditions for bi-Lipschitz A-equivalence.

Extended the Fukuda-Fukuda theorem to the Lipschitz setting.

Established a Lipschitz analogue of classical smooth equivalence results.

Abstract

In this paper, two sufficient conditions are provided for given two K-equivalent map-germs to be bi-Lipschitz A-equivalent. These are Lipschitz analogues of the known results on C^r-A-equivalence $(0 \leq r \leq \infty)$ for given two K-equivalent map-germs. As a corollary of one of our results, a Lipschitz version of the well-known Fukuda-Fukuda theorem is provided.