Topological equivalence of complex curves and bi-lipschitz homeomorphisms
type: Item
instance of: scholarly article
title: Topological equivalence of complex curves and bi-lipschitz homeomorphisms
zbMATH Open document ID: 1055.14028
author: D. Massart
published in: Michigan Mathematical Journal
publication date: 2004-06-15T00:00:00Z
review text: The author proves that two complex analytic plane or space curve germs, which are related by a bi-Lipschitz subanalytic map, are topologically equivalent, i.e., are related by a homeomorphism of neighborhoods in the ambient space. The converse is true only for plane curve germs. This extends the classical Pham-Teissier theorem [\textit{F. Pham}, Actes Congr. internat. Math. 1970, 649--654 (1971; Zbl 0245.32003)] on the bi-Lipschitz and topological equivalence of plane curve germs.
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14H50
Mathematics Subject Classification ID: 14P15
Mathematics Subject Classification ID: 32B10
zbMATH DE Number: 2075173
zbMATH Keywords: germs of complex space curves
zbMATH Keywords: topological equivalence of curve germs
zbMATH Keywords: bi-Lipschitz equivalence of analytic space germs
reviewed by: Eugenii I. Shustin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1070919562
OpenAlex ID: W1985628660
cites work: Local bi-Lipschitz classification of \(2\)-dimensional semialgebraic sets
cites work: Metric theory of semialgebraic curves
cites work: Normal embeddings of semialgebraic sets
cites work: Q3715247
cites work: Un théorème de décomposition pour les polaires génériques d'une courbe plane
cites work: Relative Lipschitz-Saturation
cites work: Invariants polaires des courbes planes
cites work: Q3700034
cites work: Lipschitz stratification of subanalytic sets
cites work: Q5639794
cites work: Q5657035
cites work: Q4486530
DOI: 10.1307/MMJ/1070919562
description: scientific article; zbMATH DE number 2075173