8 papers · 1 filter
On metric equivalence of the Brieskorn-Pham hypersurfaces
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at . Moreover we show that if two algebraic -dimensional cones $P, R\su…
Hölder invariance of the Henry-Parusinski invariant
Alexandre Fernandes, José Edson Sampaio, Joserlan Perote da Silva
In this article, we show the Hölder invariance of the Henry-Parusinski invariant. For a single germ , the Henry-Parusinski invariant of is given in terms of the leading c…
Bi-Lipschitz equivalent cones with different degrees
Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio
We show that for every there exist complex algebraic cones of dimension with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they…
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.…
Multiplicity, regularity and blow-spherical equivalence of real analytic sets
José Edson Sampaio
This article is devoted to studying multiplicity and regularity of real analytic sets. We present an equivalence for real analytic sets, named blow-spherical equivalence, which gen…