21 citations · 89 across the 23 of their papers we have counts for
23 papers · 1 filter
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…
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.…
A note on the local Lipschitz triviality of values of complex polynomial functions
Alexandre Fernandes, Vincent Grandjean, Humberto Soares
We address the question of the bi-Lipschitz local triviality of a complex polynomial function over a complex value. Our main result state that a non constant complex polynomial adm…
Multiplicity of singularities is not a bi-Lipschitz invariant
Lev Birbrair, Alexandre Fernandes, J. Edson Sampaio +1
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture, constructing examples of bi-Lipschitz equivalent complex algebraic sin…