DOI
10.11606/T.45.2019.tde-15022019-111803
Documento
Autor
Nome completo
Carlos Wilson Rodríguez Cárdenas
E-mail
Área do Conhecimento
Data de Defesa
Imprenta
São Paulo, 2018
Piccione, Paolo (Presidente)
Earp, Henrique Nogueira de Sá
Manfio, Fernando
Mossa, Roberto
Siciliano, Gaetano
Título em inglês
Genericity of bumpy metrics, bifurcation and stability in free boundary CMC hypersurfaces
Palavras-chave em inglês
Bifurcation
Bumpy metrics
Constant mean curvature
Free boundary
Jacobi operator
Stability
Resumo em inglês
In this thesis we prove the genericity of the set of metrics on a manifold with boundary M^{n+1}, such that all free boundary constant mean curvature (CMC) embeddings \varphi: \Sigma^n \to M^{n+1}, being \Sigma a manifold with boundary, are non-degenerate (Bumpy Metrics), (Theorem 2.4.1). We also give sufficient conditions to obtain a free boundary CMC deformation of a CMC inmersion (Theorems 3.2.1 and 3.2.2), and a stability criterion for this type of immersions (Theorem 3.3.3 and Corollary 3.3.5). In addition, given a one-parametric family, {\varphi _t : \Sigma \to M} , of free boundary CMC immersions, we give criteria for the existence of smooth bifurcated branches of free boundary CMC immersions for the family {\varphi_t}, via the implicit function theorem when the kernel of the Jacobi operator J is non-trivial, (Theorems 4.2.3 and 4.3.2), and we study stability and instability problems for hypersurfaces in this bifurcated branches (Theorems 5.3.1 and 5.3.3).
Título em português
Genericidade das métricas bumpy, bifurcação e estabilidade em hipersuperfícies de CMC e fronteira livre
Palavras-chave em português
Bifurcação.
Curvatura Média Constante
Fronteira Livre
Métricas Bumpy