21 citations · 89 across the 23 of their papers we have counts for
30 papers
Bi-Lipschitz characterization of space curves
Alexandre Fernandes, Zbigniew Jelonek
In the paper \cite{renato} Renato Targino shows that bi-Lipschitz type of plane curve is determined by the local ambient topological properties of curves. Here we show that it is n…
Bi-Lipschitz invariance of the multiplicity
Alexandre Fernandes, José Edson Sampaio
The multiplicity of an algebraic curve in the complex plane at a point on that curve is defined as the number of points that occur at the intersection of with a general…
Global bi-Lipschitz classification of semi-algebraic surfaces
Alexandre Fernandes, José Edson Sampaio
We classify semi-algebraic surfaces in with isolated singularities up to bi-Lipschitz homeomorphisms with respect to the inner distance. In particular, we obtain com…
On characterization of smoothness of complex analytic sets
Alexandre Fernandes, José Edson Sampaio
The paper is devoted to metric properties of singularities. We investigate the relations among topology, metric properties and smoothness. In particular, we present some higher dim…
On the Fukui-Kurdyka-Paunescu Conjecture
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
In this paper, we prove Fukui-Kurdyka-Paunescu's Conjecture, which says that subanalytic arc-analytic bi-Lipschitz homeomorphisms preserve the multiplicities of real analytic sets.…
On the extension of bi-Lipschitz mappings
Lev Birbrair, Alexandre Fernandes, Zbigniew Jelonek
Let be a closed semialgebraic set of dimension If , then there is a bi-Lipschitz and semialgebraic embedding of into Moreover, if ,…