Funcionais paramétricos elípticos em variedades riemannianas

• Ano de defesa: 2009
• Autor(a) principal: Melo, Marcelo Ferreira de
• Orientador(a): Lira, Jorge Herbert Soares de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Geometria diferencial
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/60855

It is stated that critical points of a parametric elliptic functional in a Riemannian manifold are hypersurfaces with prescrebed anisotropic mean curvature. We prove that the anisotropic Gauss map of surfaces immersed in Euclidean space with constant anisotropic mean curvature is a harmonic map. In the case of rotatioally invariat functionals in some homogeneous three-dimensional ambients, we present a abridged version of a existence result for constant anisotropic mean curvature surfaces as cylinders, spheres, tori and annuli corresponding to the anisotropic analogs of onduloids and nodoids. In the Euclidean case M¯ = R3, examples of stable critical points are provided by theWulff shapes associated to functional F. Paralleling the case of constant curvature mean spheres, a characterization of Wulff shapes is provided, which answers affirmatively a question posed by M. Koiso and B. Parmer in [13].