Lipschitz geometry and combinatorics of abnormal surface germs

Andrei Gabrielov ^[1] ; Emanoel Souza ^[2]
1. [1] Purdue University
  
  Purdue University
  
  Township of Wabash, Estados Unidos
2. [2] Universidade Federal do Ceará
  
  Universidade Federal do Ceará
  
  Brasil
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 1, 2022
Idioma: inglés
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Resumen
- We study outer Lipschitz geometry of real semialgebraic or, more general, definable in a polynomially bounded o-minimal structure over the reals, surface germs. In particular, any definable Hölder triangle is either Lipschitz normally embedded or contains some “abnormal” arcs. We show that abnormal arcs constitute finitely many “abnormal zones” in the space of all arcs, and investigate geometric and combinatorial properties of abnormal surface germs. We establish a strong relation between geometry and combinatorics of abnormal Hölder triangles.