Ambient Lipschitz equivalence of real surface singularities
| Autor: | Andrei Gabrielov, Lev Birbrair |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics Mathematics::Optimization and Control Lipschitz continuity 01 natural sciences Mathematics - Algebraic Geometry FOS: Mathematics Mathematics::Metric Geometry Gravitational singularity 0101 mathematics Topological conjugacy Equivalence (measure theory) Algebraic Geometry (math.AG) Mathematics 14B05 14P10 |
| DOI: | 10.48550/arxiv.1707.04951 |
| Popis: | We present a series of examples of pairs of singular semialgebraic surfaces (real semialgebraic sets of dimension two) in ${\mathbb R}^3$ and ${\mathbb R}^4$ which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent, but not ambient Lipschitz equivalent. For each singular semialgebraic surface $S\subset {\mathbb R}^4$, we construct infinitely many semialgebraic surfaces which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent to $S$, but pairwise ambient Lipschitz non-equivalent. Comment: 19 pages, 11 figures. Section 4 has been added in Version 2 |
| Databáze: | OpenAIRE |
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