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

作者：Sampaio J Edson^*

来源：Selecta Mathematica, New Series, 2016, 22(2): 553-559.

DOI：10.1007/s00029-015-0195-9

• Tangent cones
• Subanalytic sets
• Lipschitz regularity

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 setwhich 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.

• 出版日期2016-4