On compact surfaces with boundary, with some conditions in a conformal class, we study the problem about to find a metric with constant Gaussian curvature with boundary of constant geodesic curvature for which the regularized ...

The objetive of this work is to generalize the classic Borsuk-Ulam's Theorem. We studied there generalizations with respect to any comapact and Hausdor T- space. We used in the proofs the Z2-index of Yang and the B-index. ...

This paper deals with the surfaces of constant mean curvature in the Euclidean space. The first part of the text is devoted to minimal surfaces. We begin our studies with the Enneper-Weirstrass Representation Theorem and ...

This dissertation mainly follows the works of \cite{Gr2} and \cite{Gr5}. Considering $\mathbb{K}$ a field, algebraically closed with positive characteristic, we presented invariants of singularities in $\mathbb{K}[[\u ...

Let G be a finite group acting freely in a Hausdorff paracompact topological space X and let Y be a k-dimensional metrizable space (or k-dimensional CW-complex). In this work, by using the genus of X; gen(X;G), we prove ...

First, we introduce the basic concept of minimal surfaces and develop some results in the general theory of minimal surfaces. In the second part, we are interested in the Simon-Smith Min-Max approach to prove the existence ...

The link between braid groups on surfaces and crystallographic groups has become such an interesting topic. In the last years some advances were found in the studies of this relation, specially in the case of Artin braid ...

The main objective of this work is to prove Tverberg-type theorems and related results. More specifically, we will present an alternative proof for the Bárány-Larman conjecture for the case $r = p-1 $ with $ p $ a prime, ...

In this work, we have two objectives: the first lives in the context of the classification, up to equivariant cobordism, of the pairs (M, T) , where M is a closed and smooth manifold and T is a smooth involution ...

The present thesis is devoted to the study of closed geodesics in some types of orbifolds. First, we present the notion of Riemannian foliation and their equivalent definitions using foliation atlas and Riemannian submersions. ...