Topological equivalence of complex curves and bi-lipschitz homeomorphisms
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.
bi-Lipschitz equivalence of analytic space germs
scientific article; zbMATH DE number 2075173