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arXiv · 1707.04951

Ambient Lipschitz equivalence of real surface singularities

Lev Birbrair·Andrei Gabrielov
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Abstract

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.

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Lev Birbrair, Andrei Gabrielov. 2017-10-15. Ambient Lipschitz equivalence of real surface singularities. https://arxiv.org/abs/1707.04951

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