The goal of this dissertation is the theoretical development of the Ricci flow, a differential equation over a family of Riemannian metrics on an arbitrary differentiable manifold, and its use in the proof of the so-called ...

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 ...

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 ...

For the self-adjoint operator H, the perturbation H+A, with A also a self-adjoint operator, there is a long list of results regarding the spectrum of this perturbation. We study the spectrum of a multiplicative perturbation ...

In the present work we deal with two classes of Choquard Elliptic Equations with unbounded and sign-changing potentials, considering Fractional and Kirchhoff operators and nonlinearities with exponential critical growth. ...

Let $\Omega$ be an unbounded two dimensional strip on a ruled surface in $\mathbb{R}^d$, $d\geq2$. Consider $-\Delta_{\Omega}^{D}$ the Dirichlet Laplacian operator restricted to $\Omega$ and $-\Delta_{\Omega}^{DN}$ the ...

In this thesis, we characterize the continuity of strongly singular Calderón-Zygmund operators of type $\sigma$ in Hardy spaces, weighted Hardy spaces and Hardy-Morrey spaces in the spirit of (Coifman and Meyer, 1977). In ...

In this document, first we will introduce Persistance Homology and Category Theory basic concepts. Afterwards, we will develop the Merge Tree Theory which will be useful to keep track of connected components evolution of ...

In this work, we will find the delta shock wave solution for three Riemann problem where two are hyperbolic systems of conservation laws with linear damping and a three-component nonlinear chromatography model. We will ...

The purpose of this work is to study the Hardy spaces Hp(Rn) on euclidean spaces and your localized version, known as hp(Rn). As an application of this theory, we are going to show that Calderón-Zygmund and pseudo-differential ...