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Heat equation and the Yamabe flow on manifolds with fibered boundary metric
(Universidade Federal de São Carlos, 2021-09-02)
This work is dedicated to the study of the Yamabe flow on a class of non-compact complete Riemannian manifolds with fibered boundary and infinite volume, called Phi-manifolds. Some examples of this type of manifold include ...
Classificação de centros Hamiltonianos polinomiais biquadrados, e isocronicidade trivial versus formas canônicas para aplicações polinomiais no plano de Jacobiano unitário
(Universidade Federal de São Carlos, 2022-10-10)
This work, we classify a non- degenerate center at the origin of a planar Hamiltonian system associated to a function of the form $H(x,y)=A(x)+B(x)y^2 + C(x)y^4$, where $A$, $B$ and $C$ are polynomials. After seing a ...
Classes características de variedades topológicas e generalizadas
(Universidade Federal de São Carlos, 2022-03-24)
In this work, we will initially present generalized bundles, a concept developed by Fadell with
the objective of generalizing vector bundles, Stiefel-Whitney classes andWu’s formula from the
context of smooth manifolds ...
Geometric invariants of groups and property R-infty
(Universidade Federal de São Carlos, 2022-01-05)
In this thesis we study property R_\infty for some classes of finitely generated groups by the use of the BNS invariant \Sigma^1 and some other geometric tools. In the combinatorial chapters of the work (4, 5, 6, 10 and ...
Estabilidade, instabilidade e fenômenos de concentração em equações de reação e difusão: uma abordagem geométrica
(Universidade Federal de São Carlos, 2022-12-07)
In this work, we adress the study of stability of a reaction-difusion equation in two domains: in a family of surfaces of revolution without boundary and in a bounded open interval whose diffusion function vanishes at a ...
Não unicidade para uma classe de operadores do tipo parabólico
(Universidade Federal de São Carlos, 2022-01-18)
In this thesis we consider the non-uniqueness for a class of parabolic operators. We will
prove that for certain real analytic perturbation of the Heat Operator there is a non unique
solution for the Initial Value Problem.
Soluções positivas para equações elípticas com operadores fracionários
(Universidade Federal de São Carlos, 2022-03-18)
In this work, we present results of existence, non-existence and multiplicity of positive
solutions to elliptic problems involving the fractional p-Laplacian operator and the
fractional Laplacian in the critical case, ...
O número de Bruce-Roberts sobre uma ICIS
(Universidade Federal de São Carlos, 2022-01-19)
In this work we study the relations between the Bruce-Roberts number, $\mu_{BR}(f,X)$, the relative Bruce-Roberts, $\mu_{BR}^{-}(f,X)$, of a function germ $f\in\mathcal{O}_{n}$ over an ICIS, $(X,0)\subset (\C^{n},0)$, and ...
Polynomial Weingarten surfaces of tubular type
(Universidade Federal de São Carlos, 2022-04-04)
This work seeks to contribute to the classification of Weingarten surfaces. More precisely, it fully classifies three families of surfaces (named tubular, cyclic and canal surfaces) in a tridimensional space form (Euclidean, ...
A álgebra graduada associada a uma valorização
(Universidade Federal de São Carlos, 2021-11-30)
We begin this work with a study of the graded algebra associated to a valuation $\nu: K \longrightarrow \Gamma_{\infty}$. We verify that in the cases where the value group is free or the residue field is closed by radicals, ...