We study invariance of multiplicity of complex analytic germs and degree of complex affine
sets under outer bi‐Lipschitz transformations (outer bi‐Lipschitz homeomorphims of germs …

The multiplicity of an algebraic curve C in the complex plane at a point p on that curve is
defined as the number of points that occur at the intersection of C with a general complex …

We show that for every $ k\ge 3$ there exist complex algebraic cones of dimension $ k $
with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they …

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 …

This paper is devoted to studying the Lipschitz geometry of real analytic sets. We prove that
the relative multiplicities are bi-Lipschitz invariant, Lipschitz regular analytic curves are C 1 …

This article is devoted to studying complex algebraic sets under (global) blow-spherical
equivalence. This equivalence lives strictly between semialgebraic bi-Lipschitz equivalence …

This article is devoted to studying multiplicity and regularity of analytic sets. We present an
equivalence for analytic sets, named blow-spherical equivalence, which generalizes …

We introduce a new metric homology theory, which we call Moderately Discontinuous
Homology, designed to capture Lipschitz properties of metric singular subanalytic germs …

The aim of this paper to introduce the reader to a recent point of view on the Lipschitz
classifications of complex singularities. It presents the complete classification of Lipschitz …

In this paper we present a classification of a class of globally subanalytic CMC surfaces in
ℝ3 that generalizes the recent classification made by Barbosa and do Carmo in 2016. We …