Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann

2017/04/28 by Fernandes, Alexandre, Sampaio, J. Edson · 3 citations
#14B05 #32S50 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.00038

Abstract

We prove that tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. We also extend to real subanalytic sets the notion of reduced tangent cone and we show that subanalytic Lipschitz normally embedded sets have reduced tangent cones. In particular, we get that Lipschitz normally embedded complex analytic sets have reduced tangent cones.

Cited by

• Bi-H"older invariants in o-minimal structures
• Lipschitz geometry of the image of finite mappings
• On smoothness, tangent cones, and the metric geometry of definable sets

Related

• Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz\n homeomorphic tangent cones
• Notes on (SSP) sets
• On the link of Lipschitz normally embedded sets
• On Lipschitz rigidity of complex analytic sets
• Lipschitz geometry does not determine embedded topological type