17 citations · 44 across the 18 of their papers we have counts for
24 papers
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…
Local vs. global Lipschitz geometry
José Edson Sampaio
In this article, we prove that for a definable set in an o-minimal structure with connected link (at 0 or infinity), the inner distance of the link is equivalent to the inner dista…
Classification of real algebraic curves under blow-spherical homeomorphisms at infinity
José Edson Sampaio, Euripedes Carvalho da Silva
In this article, we present a complete classification, with normal forms, of the real algebraic curves under blow-spherical homeomorphisms at infinity.
Classification of complex algebraic curves under blow-spherical equivalence
José Edson Sampaio, Euripedes Carvalho da Silva
This article is devoted to studying complex algebraic sets under (global) blow-spherical equivalence. The main results of this article are complete classifications of complex algeb…
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 Lipschitz Geometry at infinity of complex analytic sets
José Edson Sampaio
In this article, we study the Lipschitz Geometry at infinity of complex analytic sets and we obtain results on algebraicity of analytic sets and on Bernstein's problem. Moser's Ber…
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…
On the link of Lipschitz normally embedded sets
Rodrigo Mendes, José Edson Sampaio
A path-connected subanalytic subset in is naturally equipped with two metrics: the inner and the outer metrics. We say that a subset is Lipschitz normally embedded (…
Differential invariance of the multiplicity of real and complex analytic sets
José Edson Sampaio
This paper is devoted to proving the differential invariance of the multiplicity of real and complex analytic sets. In particular, we prove the real version of Gau-Lipman's Theorem…
Some classes of homeomorphisms that preserve multiplicity and tangent cones
J. Edson Sampaio
In this paper we present some applications of A'Campo-Lê's Theorem and we study some relations between Zariski's Questions A and B. It is presented some classes of homeomorphisms t…
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…
On Zariski's multiplicity problem at infinity
J. Edson Sampaio
We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must h…
Multiplicity and degree as bi-Lipschitz invariants for complex sets
Javier Fernández de Bobadilla, Alexandre Fernandes, J. Edson Sampaio
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…
On Lipschitz rigidity of complex analytic sets
Alexandre Fernandes, J. Edson Sampaio
We prove that any complex analytic set in which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^…
Tangent cones of Lipschitz normally embedded sets are Lipschitz normally embedded. Appendix by Anne Pichon and Walter D. Neumann
Alexandre Fernandes, J. Edson Sampaio
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 s…
Hölder equivalence of complex analytic curve singularities
Alexandre Fernandes, J. Edson Sampaio, Joserlan P. Silva
We prove that if two germs of irreducible complex analytic curves at have different sequence of characteristic exponents, then there exists such that tho…
Multiplicity, regularity and blow-spherical equivalence of complex analytic sets
J. Edson Sampaio
This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical set…
Multiplicity of analytic hypersurface singularities under bi-Lipschitz homeomorphisms
Alexandre Fernandes, J. Edson Sampaio
We give partial answers to a metric version of Zariski's multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) si…
Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones
J. Edson Sampaio
We prove that if there exists a bi-Lipschitz homeomorphism (not necessarily subanalytic) between two subanalytic sets, then their tangent cones are bi-Lipschitz homeomorphic. As a…