Now showing items 1-12 of 12

    • Globally subanalytic CMC surfaces in $\mathbb{R}^3$ with singularities 

      Sampaio, J.E. (2020-03-02)
      In this paper we present a classification of a class of globally subanalytic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016. We show that a globally subanalytic ...
    • Hölder equivalence of complex analytic curve singularities 

      Fernandes, A.; Sampaio, J.E.; Silva, J.P. (2018-08-06)
      We prove that if two germs of irreducible complex analytic curves at $0\in\mathbb{C}^2$ have different sequence of characteristic exponents, then there exists $0<\alpha<1$ such that those germs are not $\alpha$-H\"older ...
    • Multiplicity and degree as bi‐Lipschitz invariants for complex sets 

      Fernandes, A.; Fernández de Bobadilla, J.Autoridad BCAM; Sampaio, J.E. (2018-08-29)
      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 in the first case and outer bi-Lipschitz ...
    • Multiplicity of singularities is not a bi-Lipschitz invariant 

      Birbrair, L.; Fernandes, A.; Sampaio, J.E.; Verbitsky, M. (2020-01-17)
      It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.
    • Multiplicity, regularity and blow-spherical equivalence of complex analytic sets 

      Sampaio, J.E. (2020-01-29)
      This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain several applications with this new ...
    • On Lipschitz rigidity of complex analytic sets 

      Fernandes, A.; Sampaio, J.E. (2019-02-26)
      We prove that any complex analytic set in $\mathbb{C}^n$ which is Lipschitz normally embedded at infinity and has tangent cone at infinity that is a linear subspace of $\mathbb{C}^n$ must be an affine linear subspace of ...
    • On Zariski’s multiplicity problem at infinity 

      Sampaio, J.E. (2018-08-14)
      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 have the same degree. More specifically, ...
    • A proof of the differentiable invariance of the multiplicity using spherical blowing-up 

      Sampaio, J.E. (2018-04-21)
      In this paper we use some properties of spherical blowing-up to give an alternative and more geometric proof of Gau-Lipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, ...
    • Semialgebraic CMC surfaces in $\mathbb{R}^3$ with singularities 

      Sampaio, J.E. (2018-06-30)
      In this paper we present a classification of a class of semialgebraic CMC surfaces in $\mathbb{R}^3$ that generalizes the recent classification made by Barbosa and do Carmo in 2016 (complete reference is in the paper), we ...
    • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

      Sampaio, J.E. (2018-08-19)
      In this paper it is presented some classes of homeomorphisms that preserve multiplicity and tangent cones of complex analytic sets. Moreover, we present a class of homeomorphisms that has the multiplicity as an invariant ...
    • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

      Sampaio, J.E. (2019-05-28)
      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 that preserve multiplicity and tangent cones ...
    • Some classes of homeomorphisms that preserve multiplicity and tangent cones 

      Sampaio, J.E. (2020-01-01)
      In this paper we present some applications of A’Campo-Lˆe’s Theorem and we study some relations between Zariski’s Questions A and B. It is presented some classes of homeomorphisms that preserve multiplicity and tangent ...