Now showing items 1-13 of 13

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

(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 ﻿

(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 ...
• #### Moderately Discontinuous Homology ﻿

(2021-01-01)
We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of metric singular subanalytic germs. The main novelty of our approach is to allow ...
• #### Multiplicity and degree as bi‐Lipschitz invariants for complex sets ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...