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Mathematics > Metric Geometry

arXiv:2201.06132 (math)
[Submitted on 16 Jan 2022 (v1), last revised 20 Jul 2022 (this version, v2)]

Title:Lipschitz geometry of pairs of normally embedded Hölder triangles

Authors:Lev Birbrair, Andrei Gabrielov
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Abstract:We consider a special case of the outer bi-Lipschitz classification of real semialgebraic (or, more general, definable in a polynomially bounded o-minimal structure) surface germs, obtained as a union of two normally embedded Hölder triangles. We define a combinatorial invariant of an equivalence class of such surface germs, called $\sigma\tau$-pizza, and conjecture that, in this special case, it is a complete combinatorial invariant of outer bi-Lipschitz equivalence.
Comments: 24 pages, 7 figures
Subjects: Metric Geometry (math.MG); Algebraic Geometry (math.AG)
MSC classes: 51F30, 14P10, 03C64
Cite as: arXiv:2201.06132 [math.MG]
  (or arXiv:2201.06132v2 [math.MG] for this version)
  https://doi.org/10.48550/arXiv.2201.06132

Submission history

From: Andrei Gabrielov [view email]
[v1] Sun, 16 Jan 2022 20:18:44 UTC (151 KB)
[v2] Wed, 20 Jul 2022 13:16:07 UTC (156 KB)
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