DSpace Coleção:http://www.repositorio.ufc.br/handle/riufc/652021-08-04T02:22:33Z2021-08-04T02:22:33ZVariedades quasi-Einstein compactas com bordoSousa, Tiago Gadelha dehttp://www.repositorio.ufc.br/handle/riufc/597942021-08-01T00:39:48Z2021-06-04T00:00:00ZTítulo: Variedades quasi-Einstein compactas com bordo
Autor(es): Sousa, Tiago Gadelha de
Abstract: The objective of this work is to study compact quasi-Einstein manifolds with edge. In the first part, we will provide edge estimates and geometric obstruction results. We establish a sharp upper estimate for the edge area of a compact quasi-Einstein manifold with a connected edge assuming a lower bound of the Ricci curvature of the edge. With equality being valid if, and only if, the boundary of the manifold is isometric to a sphere. The result is still valid in the three-dimensional case without the condition of limiting the Ricci curvature of the border. Considering a compact quasi-Einstein manifold with (possibly disconnected) edge and constant scalar curvature, we were also able to obtain a characterization result in terms of surface gravity of the edge components. For the case where the edge is connected, a sharp geometric inequality ensues from this result involving the edge area and the volume of such manifolds, which can also be seen as a result of obstruction. Furthermore, equality occurs if, and only if, the manifold is isometric, unless scaling, to the hemisphere. We conclude the first part of this work by presenting an upper edge estimate for compact quasi-Einstein manifolds with a (possibly disconnected) edge in terms of the Brown-York mass. In the second part of this work, we provide a Böchner-type formula for quasi-Einstein manifolds with a dimension greater than or equal to 3 which allows us to obtain stiffness results assuming a pinched condition involving the traceless Ricci tensor. Furthermore, considering the Yamabe invariant (or the Yamabe constant), which is an important tool in prescribed metric problems, we obtain an integral curvature estimate in terms of the Yamabe constant for 4-dimensional compact quasi-Einstein manifolds with boundary and constant scalar curvature.2021-06-04T00:00:00ZGráficos solitons do fluxo da curvatura média.Sena, Renivaldo Sodré dehttp://www.repositorio.ufc.br/handle/riufc/514242020-08-28T13:58:15Z2018-09-26T00:00:00ZTítulo: 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.2019-07-26T00:00:00Z