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On the classification of two dimensional flows
(Universidade Federal de São Carlos, 2023-08-02)
Lawrence Markus, a well-known mathematician, published, in 1954, a strong result about classification of planar vector fields. Afterwards, Dean Arnold Neumann generalized such work for continuous flows, and the result ...
Campos de Yang-Mills fracamente estáveis na esfera de dimensão quatro
(Universidade Federal de São Carlos, 2023-05-03)
In this work we made a quick study on some basic results related to Groups and Lie Algebras,
action of Groups and Fiber Bundles with the objective of defining connections in Principal Bundles
and, later, in Associated ...
Algumas aplicações de p-pontos
(Universidade Federal de São Carlos, 2023-08-24)
In this work we analyze the concept of \(p\)-points in \(\omega\) and its relation with forcing, in particular Sacks forcing and side-by-side Sacks forcing. With this we verify that the existence of \(p\)-points with ...
Um princípio de tangência e aplicações
(Universidade Federal de São Carlos, 2021-12-17)
We present tools, such as a maximum principle for elliptic functions and properties of a-hyperbolic polynomials, to study a tangency principle between two hypersurfaces with r-mean curvatures of a Riemannian manifold, which ...
Categoria de Lusternik-Schnirelmann e aplicações
(Universidade Federal de São Carlos, 2022-02-14)
The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation ...
Germes de funções sobre variedades analíticas
(Universidade Federal de São Carlos, 2006-03-03)
The study of analytic germs of functions (Cn, 0) → (C, 0) under R - equivalence relation is a central point in Singularity Theory and the information we have in this direction is very rich. In this dissertation we ...
Folheações riemannianas e geodésicas fechadas em orbifolds
(Universidade Federal de São Carlos, 2016-03-04)
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. ...
Determinante regularizado do Laplaciano e conjuntos isoespectrais em superfícies
(Universidade Federal de São Carlos, 2019-02-27)
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 ...
Aspectos homológicos e homotópicos do teorema de Borsuk-Ulam
(Universidade Federal de São Carlos, 2011-02-20)
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. ...
Superfícies de Curvatura Média Constante no Espaço Euclidiano
(Universidade Federal de São Carlos, 2019-03-19)
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 ...