Lipschitz geometry of pairs of normally embedded Hölder triangles

2022/01/16 by Birbrair, Lev, Gabrielov, Andrei
#03C64 #14P10 #51F30 #Algebraic Geometry (math.AG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2201.06132

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 στ-pizza, and conjecture that, in this special case, it is a complete combinatorial invariant of outer bi-Lipschitz equivalence.

Related

• Outer Lipschitz Classification of Normal Pairs of Hölder Triangles
• Lipschitz geometry and combinatorics of abnormal surface germs
• Lipschitz Geometry of Real Semialgebraic Surfaces
• Ambient Lipschitz geometry of normally embedded surface germs
• Universality theorem for LNE Hölder triangles