Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones

• J. Edson Sampaio ^[1]
  1. [1] Universidade Federal do Ceará

     Universidade Federal do Ceará

     Brasil

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 553-559
• Idioma: inglés
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• Resumen

  • We prove that if there exists a bi-Lipschitz homeomorphism (not necessarily subanalytic) between two subanalytic sets, then their tangent cones are bi-Lipschitz homeomorphic. As a consequence of this result, we show that any Lipschitz regular complex analytic set, i.e., any complex analytic set which is locally bi-Lipschitz homeomorphic to an Euclidean ball must be smooth. Finally, we give an alternative proof of S. Koike and L. Paunescu’s result about the bi-Lipschitz invariance of directional dimensions of subanalytic sets.