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

## TL;DR

This paper proves that tangent cones of Lipschitz normally embedded sets retain the Lipschitz normally embedded property and extends related concepts to real subanalytic and complex analytic sets, highlighting their geometric structure.

## Contribution

It establishes that tangent cones of Lipschitz normally embedded sets are also Lipschitz normally embedded and introduces the notion of reduced tangent cones for subanalytic sets.

## Key findings

- Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded.
- Subanalytic Lipschitz normally embedded sets have reduced tangent cones.
- Lipschitz normally embedded complex analytic sets have reduced tangent cones.

## 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.