## Search

Now showing items 1-10 of 13

#### 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 ...

#### 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 ...

#### 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 ...

#### 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.

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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, ...