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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 ...
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 ...
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 ...
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 ...
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 ...
Invariantes de singularidades em característica positiva
(Universidade Federal de São Carlos, 2020-03-30)
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 ...
Equisingularidades de funções definidas em ICIS e IDS
(Universidade Federal de São Carlos, 2020-03-10)
We study the equisingularity of a family of function germs $\{f_t\colon(X_t,0)\to (\mathbb{C},0)\}$, where $\{(X_t,0)\}$ is a family of $d$-dimensional isolated determinantal singularity. We define the $(d-1)$th polar ...
Sobre teoremas do tipo Tverberg
(Universidade Federal de São Carlos, 2020-12-17)
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, ...
Grupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos
(Universidade Federal de São Carlos, 2020-12-07)
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 ...