Princípio do máximo relacionado ao crescimento de volume

• Ano de defesa: 2022
• Autor(a) principal: Rodrigues, Matheus Mendes
• Orientador(a): Muniz Neto, Antonio Caminha
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Princípio do máximo (Matemática); Variedades riemannianas; Crescimento de volume; Resultados tipo-Bernstein; Hipersuperfícies com curvatura média constante; Subvariedades mínimas; Maximum principle (Mathematics); Riemannian manifolds; Volume growth; Bernstein-type results; Constant mean curvature hypersurfaces; Minimal submanifolds
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/67268

In this Dissertation, it is presented a new form of maximum principle for smooth functions on a complete noncompact Riemannian manifold M for which there exists a bounded vector field X such that its inner product with the gradient of a function f is greather than or equal to zero on M and its divergent is greather than or equal af outside a suitable compact subset of M, for some positive constant a, under the assumption that M has either polynomial or exponential volume growth. We then use it to obtain some Bernstein-type results for hypersurfaces immersed into a Riemannian manifold endowed with a Killing vector field, as well as to obtain some results on the existence and the size of minimal submanifolds immersed into a Riemannian manifold endowed with a closed conformal vector field.