DSpace Coleção: PPGMAT
https://repositorio.ufpb.br/jspui/handle/tede/6873
PPGMATWed, 20 Nov 2019 18:19:07 GMT2019-11-20T18:19:07Zp−parabolic submanifolds in certain spacetimes: rigidity, uniqueness and non-existence results
https://repositorio.ufpb.br/jspui/handle/123456789/15498
Título: p−parabolic submanifolds in certain spacetimes: rigidity, uniqueness and non-existence results
Autor(es): Roing, Fernanda
Primeiro Orientador: Lima Júnior, Eraldo Almeida
Abstract: In this work we present rigidity and uniqueness results for parabolic and stable constant mean curvature hypersurfaces immersed in Generalized Robertson-Walker and Standard Static spacetimes. We obtained some conditions under which a hypersurface in these ambiences must be parabolic, as well as stable. In order to achieve the uniqueness results, we used some cut-o functions coming from the parabolicity jointly with the stability operator. Also, we introduced the concept of totally trapped submanifold and obtained some uniqueness and non-existence results when the submanifold is p-parabolic. We also presented a lemma of type Nishikawa in order to obtain CalabiBerstein type results for surfaces in Robertson-Walker Generalized spacetimes.
Editor: Universidade Federal da Paraíba
Tipo: TeseFri, 22 Feb 2019 00:00:00 GMThttps://repositorio.ufpb.br/jspui/handle/123456789/154982019-02-22T00:00:00ZQualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent
https://repositorio.ufpb.br/jspui/handle/123456789/15373
Título: Qualitative properties of positive singular solutions to nonlinear elliptic systems with critical exponent
Autor(es): Caju, Rayssa Helena Aires de Lima
Primeiro Orientador: Ó, João Marcos Bezerra do
Abstract: In this work we study the asymptotic behavior to positive solutions of the following coupled elliptic system of nonlinear Schrödinger equations
∆gui −
2 X j=1
Aij(x)uj +
n(n−2) 4 |U|
4 n−2ui = 0
which are deﬁned in the punctured unit ball B1(0)\{0} for n ≥ 3. Here g is a Riemannian metric on the unit ball and the potential A is assumed a C1 map such that Aij(x) is a symmetrical matrix for each x in B1(0). From the viewpoint of conformal geometry, this systems are pure extensions of Yamabe-type equations. We will approach the problem assuming ﬁrst that g is the euclidian metric and the potential A vanishes. In this case we are able to prove that the solutions of our problem are asymptotics to what we call Fowler-type solutions. In the general case we will prove the same result by putting some restrictions on the potential and assuming that the dimension is less or equal to ﬁve.
Editor: Universidade Federal da Paraíba
Tipo: TeseFri, 23 Feb 2018 00:00:00 GMThttps://repositorio.ufpb.br/jspui/handle/123456789/153732018-02-23T00:00:00ZCotas para o número máximo de retas duas a duas disjuntas em uma família S
https://repositorio.ufpb.br/jspui/handle/123456789/15079
Título: Cotas para o número máximo de retas duas a duas disjuntas em uma família S
Autor(es): Ferreira, Mariana de Lima
Primeiro Orientador: Arancibia, Jacqueline Fabiola Rojas
Abstract: Let r(S) be the maximum number of pairwise disjunct lines that a non-singular surface S ⊂ P3 contains and rd = max {r(S) | deegre(S) = d}. Ensure that r(S) = 6 for all non-singular cubic surface S, therefore r3 = 6. For d = 4, r4 = 16, it was showed by the Russian mathematician Viacheslav Nikulin in [9]. We quote that Rojas-Santos in [7], obtained that r(F) = 16 if F is the Schur’s quartic. At the moment rd is unknown for d ≥ 5. In this work we aim to present bounds for the maximum number of two-by-two disjunct straight lines in the family S whose members are the deegre d non-singular surfaces Sd ⊂ P3 deﬁnided by φ(x0,x1)−φ(x2,x3) being φ(u,v) = uv(ud−2−vd−2) and d ≥ 5. In fact, for d odd we show that r(Sd) = d(d−2) + 4, however Boiss´ere-Sarti proved that r(Sd) ≥ d(d−2) + 4 when d is odd and d ≥ 7 in [3]. For the even case, we obtain d(d−2) + 4 ≤ r(Sd) ≤ d(d−2) + d2 2 if d 6= 6 and r(S6) = 48. Considering the bound rd ≤ d(d−2) for all d ≥ 4 given by the Japanese mathematician Miyaoka in [8], we conclude as soon as r6 = 48.
Editor: Universidade Federal da Paraíba
Tipo: DissertaçãoFri, 20 Jul 2018 00:00:00 GMThttps://repositorio.ufpb.br/jspui/handle/123456789/150792018-07-20T00:00:00ZCurvas de Peano, lineabilidade, espaçabilidade e algebrabilidade
https://repositorio.ufpb.br/jspui/handle/123456789/14968
Título: Curvas de Peano, lineabilidade, espaçabilidade e algebrabilidade
Autor(es): Santos Filho, Sérgio Roméro Vital dos
Primeiro Orientador: Albuquerque, Nacib André Gurgel e
Abstract: In this dissertation, we turn our attention to the space of the continuous surjections between euclidean spaces. We constructed a Peano curve, also known as a space ll curve, and proved a result of optimal lineability from the point of view of dimension. Then we prove some properties on the order of growth of whole functions and we deal with the problem of algebrability, proving that the space of continuous surjections with complex values is strongly maximal algebrable. Subsequently, we prove the spaceability of the Peano curves between euclidean spaces andwe nalize our work by bringing some generalizations of the presented results to topological vector spaces that are continuous image of the real line.
Editor: Universidade Federal da Paraíba
Tipo: DissertaçãoFri, 23 Feb 2018 00:00:00 GMThttps://repositorio.ufpb.br/jspui/handle/123456789/149682018-02-23T00:00:00Z