Alexandre Fernandes
Federal University of Ceará
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Publication
Featured researches published by Alexandre Fernandes.
Qualitative Theory of Dynamical Systems | 2004
Alexandre Fernandes; Carlos Gutierrez; Roland Rabanal
There are obtained conditions under which maps fromRn to itself are globally injective. In particular there are proved some partial results related to the Weak Markus-Yamabe Conjecture which states that if a vector field X:Rn →Rn has the property that, for allp ∈Rn, all the eigenvalues ofD X (p) have negative real part, thenX has at most one singularity.
Mathematische Annalen | 2008
Lev Birbrair; Alexandre Fernandes; Walter D. Neumann
We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.
Geometriae Dedicata | 2009
Lev Birbrair; Alexandre Fernandes; Walter D. Neumann
We discuss the bi-Lipschitz geometry of an isolated singular point of a complex surface with particular emphasis on when it is metrically conical.
Proceedings of the American Mathematical Society | 2007
Lev Birbrair; João Carlos Ferreira Costa; Alexandre Fernandes; M. A. S. Ruas
In this paper we prove that the set of equivalence classes of germs of real polynomials of degree less than or equal to k, with respect to κ-bi-Lipschitz equivalence, is finite.
Selecta Mathematica-new Series | 2010
Lev Birbrair; Alexandre Fernandes; Walter D. Neumann
An explanation is given for the initially surprising ubiquity of separating sets in normal complex surface germs. It is shown that they are quite common in higher dimensions too. The relationship between separating sets and the geometry of the metric tangent cone of Bernig and Lytchak is described. Moreover, separating sets are used to show that the inner Lipschitz type need not be constant in a family of normal complex surface germs of constant topology.
Journal of Topology | 2016
Alexandre Fernandes; J. Edson Sampaio
We give partial answers to a metric version of Zariskis multiplicity conjecture. In particular, we prove the multiplicity of complex analytic surface (not necessarily isolated) singularities in
arXiv: Algebraic Geometry | 2010
Lev Birbrair; Alexandre Fernandes; Walter D. Neumann
\mathbb{C}^3
Open Mathematics | 2010
Sérgio Alvarez; Lev Birbrair; João Carlos Ferreira Costa; Alexandre Fernandes
is a bi-Lipschitz invariant.
Journal of Topology | 2018
Javier Fernández de Bobadilla; Alexandre Fernandes; J. Edson Sampaio
We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.
arXiv: Algebraic Geometry | 2012
Alexandre Fernandes; Maria Aparecida Soares Ruas
We study the topological K-equivalence of function-germs (ℝn, 0) → (ℝ, 0). We present some special classes of piece-wise linear functions and prove that they are normal forms for equivalence classes with respect to topological K-equivalence for definable functions-germs. For the case n = 2 we present polynomial models for analytic function-germs.