DSpace Coleção:http://www.repositorio.ufc.br/handle/riufc/652020-06-03T23:30:21Z2020-06-03T23:30:21ZGráficos solitons do fluxo da curvatura média.Sena, Renivaldo Sodré dehttp://www.repositorio.ufc.br/handle/riufc/514242020-04-24T17:08:57Z2018-09-26T00:00:00ZTítulo: Gráficos solitons do fluxo da curvatura média.
Autor(es): Sena, Renivaldo Sodré de
Abstract: We investigate the existence of graphs that are solitons for the ﬂow of the mean curvature. Under some assumptions, we prove the existence of solitons in warped products I × h M. We also prove a Jenkins-Serrin type result, which gives conditions for the non existence of Dirichlet solution problem for the soliton graph equation. Finally, we study soliton graphs of the mean curvature in the warped product M × h R .2018-09-26T00:00:00ZLipschitz geometry of complex plane algebraic curves.Targino, Renato Oliveirahttp://www.repositorio.ufc.br/handle/riufc/505372020-03-05T16:51:08Z2020-02-13T00:00:00ZTítulo: Lipschitz geometry of complex plane algebraic curves.
Autor(es): Targino, Renato Oliveira
Abstract: We present the complete classiﬁcation of complex plane algebraic curves, equipped with the induced Euclidean metric, up to global bilipschitz homeomorphism. In particular, we prove a theorem giving a complete classiﬁcation of the Lipschitz geometry at inﬁnity of complex algebraic plane curves. We synthesize combinatorial objects that encode both Lipschitz geometry and Lipschitz geometry at inﬁnity of complex algebraic plane curves.2020-02-13T00:00:00ZEstimativas do gradiente na fronteira para soluções de desigualdades diferenciais totalmente não lineares.Gomes, Diego Eloi Misquitahttp://www.repositorio.ufc.br/handle/riufc/482292019-12-06T16:18:48Z2019-07-26T00:00:00ZTítulo: Estimativas do gradiente na fronteira para soluções de desigualdades diferenciais totalmente não lineares.
Autor(es): Gomes, Diego Eloi Misquita
Abstract: In this work we obtain an estimate and a regularity of the gradient for solutions to fully nonlinear diﬀerential inequalities with unbounded coeﬃcients and quadratic growth on the gradient. The boundary data is C^(1,Dini) and solutions are understood in the viscosity sense. More speciﬁcally, the drift term and the RHS are in L^q with q>n. We prove that u ∈ C^1 on the ﬂat boundary with some modulus of continuity with the estimates. Our results can be seen as extended versions of remarkble estimates obtained by N. Krylov (1983) and O. Ladyzhenskaya and N. Ural’tseva (1989). Finally, we also show that in the case RHS is in L^n the result does not hold and solutions may fail to be even Lipschitz on a neighborhood of the boundary wich means that, in the RHS sense, this theorem is sharp.2019-07-26T00:00:00ZProblems about mean curvatureGama, Eddygledson Souzahttp://www.repositorio.ufc.br/handle/riufc/450032019-08-22T13:25:59Z2019-07-25T00:00:00ZTítulo: Problems about mean curvature
Autor(es): Gama, Eddygledson Souza
Abstract: This thesis is divided into three chapters. In the ﬁrst chapter, it is done a brief introduction of the main tools necessary for the development of this work. In turn, in the second chapter it develops the Jenkins-Serrin theory for vertical and horizontal cases. Regarding the vertical case, it only proves the existence of the solution of Jenkins-Serrin problem for the type I, when M is rotationally symmetric and has non-positive sectional curvatures.However, with respect to the horizontal case, the existence and the uniqueness is proved
in a general way, namely a.ssuming that the base space M has a particular structure. The ing solitons in R
n+1 . More precisely, it is proved that the unique examples C 1 −asymptotic to two half-hyperplanes outside a cylinder are the hyperplanes parallel to e n+1 and the elements of the family associated with the tilted grim reaper cylinder in R n+1 .2019-07-25T00:00:00Z