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

Joao Carlos Ferreira Costa; Takashi Nishimura; Maria Aparecida Soares Ruas

doi:10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3

paper

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

arXiv:1302.4778 · doi:10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3 10.1007/s13398-012-0105-3

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.

Published online in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 2012