Rigidez de superfícies fechadas que minimizam área em variedades tridimensionais

• Autor(a) principal: Santos, Franciele Conrado dos
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFS
• Texto Completo: http://ri.ufs.br/jspui/handle/riufs/12503
• topic: Matemática; Superfícies; Curvas; Cônicas; Espaço e tempo; Variedades tridimensionais; Curvatura escalar; Superfícies mínimas; Rigidez; 3-manifolds; Scalar curvature; Minimal surfaces; Rigidity; CIENCIAS EXATAS E DA TERRA::MATEMATICA

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.