Topological equivalence of complex curves and bi-lipschitz homeomorphisms (Q1432732)
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scientific article; zbMATH DE number 2075173
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Topological equivalence of complex curves and bi-lipschitz homeomorphisms |
scientific article; zbMATH DE number 2075173 |
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Topological equivalence of complex curves and bi-lipschitz homeomorphisms (English)
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15 June 2004
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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.
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germs of complex space curves
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topological equivalence of curve germs
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bi-Lipschitz equivalence of analytic space germs
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