DSpace Coleção:http://ri.ufs.br/jspui/handle/riufs/24692020-09-27T20:30:12Z2020-09-27T20:30:12ZRigidez de superfícies fechadas que minimizam área em variedades tridimensionaisSantos, Franciele Conrado doshttp://ri.ufs.br/jspui/handle/riufs/125032019-12-19T22:19:54Z2016-03-04T00:00:00ZTítulo: Rigidez de superfícies fechadas que minimizam área em variedades tridimensionais
Autor(es): Santos, Franciele Conrado dos
Abstract: The main task of this work is to study the results established in the papers [2], [3], [28] and [6].
Roughly speaking, these papers work with Riemannian 3-manifolds with lower bounded scalar
curvature which have locally area-minimizing closed surfaces. Such surfaces may be homeomorphic
to the sphere, to the projective plane, to the torus or to the hyperbolic surfaces. In the paper [6], Cai
and Galloway have considered the case in which the surface is a 2-sided torus. They showed under
the assumption that the scalar curvature is nonnegative that the manifold is
at in a neighborhood
of the surface. In the other cases, Bray-Brendle-Eichmair-Neves [2], Bray-Brendle-Neves [3] and
Nunes [28] have obtained inequalities involving the scalar curvature of the manifold, the area of
the surface and its Euler characteristic. Furthermore, they characterize the manifold in case of
equality.2016-03-04T00:00:00ZUm problema de extensão relacionado ao laplaciano fracionário e aplicaçõesCarvalho, Jonison Lucas dos Santoshttp://ri.ufs.br/jspui/handle/riufs/124102019-11-20T22:23:06Z2016-12-05T00:00:00ZTítulo: Um problema de extensão relacionado ao laplaciano fracionário e aplicações
Autor(es): Carvalho, Jonison Lucas dos Santos
Abstract: The Laplacian operator positivity allows its square roots de nition and this relates
directly to the problem of harmonious extension in the superior semi-space, like
an operator that takes the condition from Dirichlet's outline to the Neumann's condition.
In this work, that was based on results developed by Ca areli and Silvestre
[8], we got similar characterization for the Fractional Laplacian Operator. In addition,
we apply the characterization reported to the sdudy of existence of non-trivial
solution of the non-linear fractional Schrodinger equation.2016-12-05T00:00:00ZSobre equações integrais de evolução e aplicaçõesSantos, Jucileide doshttp://ri.ufs.br/jspui/handle/riufs/119502019-09-26T19:12:57Z2019-08-23T00:00:00ZTítulo: Sobre equações integrais de evolução e aplicações
Autor(es): Santos, Jucileide dos
Abstract: Motivated by the huge success of the applications of the Evolutionary Integral
Equations in many areas of engineering and the fact that the literature has several
open problems, in this work we aimed to study the theory involving abstract
Volterra equations as well as issues related to a Cauchy fractional problem of
order 0<α<1. In this last one we try to answer some questions about the
global well-posedness and self-similarity of the solutions.2019-08-23T00:00:00ZCongruências de retas e equações das superfícies principaisSantos, Igor Chagashttp://ri.ufs.br/jspui/handle/riufs/115952019-07-26T19:46:52Z2019-02-21T00:00:00ZTítulo: Congruências de retas e equações das superfícies principais
Autor(es): Santos, Igor Chagas
Abstract: Motivated by Monge, which in [10] presented the principal configuration of tri-axial ellipsoid,
and by Sotomayor and Gutierrez, which in [12], using the Qualitative Theory of
O.D.E.’s rigorously established the configuration of the lines of curvature in neighborhoods
of umbilic points, our objective is, considering the congruence of lines generated by
the restriction to the Ellipsoid of a linear field with three real, distinct and nonzero eigenvalues
or two complex conjugate eigenvalues and one nonzero real eigenvalue, to study
the behavior of the principal curves of the congruence on the Ellipsoid. In this context,
Bianchi [1], Eisenhart [6], Forsyth [8], Pottmann and Wallner [17] and Weatherburn [22]
are our references for the Theory of Congruences of Lines . The principal curves are
integral curves of a Binary Differential Equation, hence, Bruce and Fidal [2] and Bruce
and Tari [3] are our references to study the local the behavior of these curves in neighborhoods
of special points, that we will call Umbilic Singularities of the Congruence. In
the final chapter, what we intend to present as contribution of this study are the possible
configurations of the principal curves of the congruence in the Ellipsoid for the considered
congruences.2019-02-21T00:00:00Z