Hipersuperfícies Capilares Estáveis em um Semiespaço ou em um Slab

• Autor(a) principal: SILVA, Márcio Eduardo Gonçalves
• Data de Publicação: 2018
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFMA
• Texto Completo: https://tedebc.ufma.br/jspui/handle/tede/tede/2874
• topic: Hipersuperfícies Capilares;; Hipersuperfície com curvatura média constante;; Estabilidade;; Semiespaço;; Slab; Capillary Hypersurfaces;; Constant mean curvature hypersurfaces;; Stability;; Half-Space;; Slab; Geometria e Topologia

This work presents and analyzes the results obtained by Abdelhamid Ainouz and Rabah Souam [1]. They obtained three results for immersed hypersurfaces in a domains in Euclidean space such as slab and half-space. The general result is that stable immersed capillary hypersurfaces in a closed slab or a closed half-space in Rn+1 have a rotational symmetry. More specifically, with the capillarity and stability hypothesis, they have demonstrated that an immersed surfaces of genus zero in a slab of R3, it is of revolution; When the immersed hypersurface in a slab of Rn, n 2, with free boundary and the boundary components are embedded, it is either a circular vertical cylinder or a graph over boundary domain, lastly, when the immersed hypersurface in the semispace of Rn, n 2, with contact angle 0 < /2 and the boundary components are embedded, it is spherical cap.