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Previous issue date: 2017-06-20 / Vamos generalizar um Princípio do Máximo no Infinito no caso parabólico dado por Ronaldo F. de Lima em seu trabalho A Maximum Principles at Infinity for surfaces with Constant Mean Curvature in Euclidean Space e por Ronaldo F. de Lima e William Meeks no artigo Maximum Principles at Infinity for surfaces of Bounded Mean Curvature in R³ and H³ onde agora teremos hipersuperfícies M₁ e M₂ do Rⁿ⁺¹, disjuntas com bordos (possivelmente vazios) ∂M₁ e ∂M₂, de curvatura média limitada com um Contato Ideal no Infinito, porém agora sem restrição sobre a curvatura Gaussiana de qualquer hipersuperfície. Como aplicação geométrica apresentaremos alguns resultados que estendem para hipersuperfícies mergulhadas M₁ e M₂ do Rⁿ⁺¹ com bordos vazios, uma generalização do Princípio do Máximo de Hopf para hipersuperfícies disjuntas que se aproximam assintoticamente. Uma vez obtidos esses resultados, introduzimos uma estrutura de variedade Riemanniana ponderada em Rⁿ⁺¹ e obtemos algumas generalizações dos resultados antes obtidos sob hipóteses dos objetos agora existentes, tais como f-curvatura média, f -Laplaciano, variedades ponderadas f-parabólicas, para as hipersuperfícies M₁ e M₂ do Rfⁿ⁺¹ . / We will generalize a Maximum Principle at Infinity in the parabolic case given in paper A Maximum Principles at Infinity for surfaces with Constant Mean Curvature in Euclidean Space by Ronald F. de Lima and Ronaldo F. de Lima and William Meeks in paper Maximum Principles at Infinity for surfaces of Bounded Mean Curvature in R³ and H³ where we will now have hypersurfaces M₁ and M₂ of Rⁿ⁺¹ disjoints, with boundary (possibly empty) ∂M₁ e ∂M₂ of the bounded mean curvature and with Ideal Contact et Infinity, but now without restrictions on the Gaussian Curvature of any hypersurface. As geometric application we will present some results that extend for embedded hypersurfaces M₁ and M₂ in Rⁿ⁺¹ with empty boundaries a generalization of Hopf’s Maximum Principle for disjoint hypersurfaces that get close asymptotically. Once obtained these results, we inserted a structure of a weighted Riemannian Manifold in Rⁿ⁺¹ and obtained some generalizations of the results previously achieved under some hypothesis of the objects now found, such as f-mean curvature, f-Laplacian, f–parabolic weighted manifold, in the hypersurfaces M₁ and M₂ from Rfⁿ⁺¹ .
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufpe.br:123456789/25480 |
| Date | 20 June 2017 |
| Creators | SILVA, José Deibsom da |
| Contributors | http://lattes.cnpq.br/2467726574611453, SOUSA, Antonio Fernando Pereira de |
| Publisher | Universidade Federal de Pernambuco, Programa de Pos Graduacao em Matematica, UFPE, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFPE, instname:Universidade Federal de Pernambuco, instacron:UFPE |
| Rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil, http://creativecommons.org/licenses/by-nc-nd/3.0/br/, info:eu-repo/semantics/openAccess |
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