Teorema de Bersntein para gráficos mínimos em R^n, (3,<=n,,=6)

• Ano de defesa: 2014
• Autor(a) principal: Edno Alan Pereira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Superfícies Mínima; Estabilidade; Teorema de Bernstein; Matemática; Riemannian, geometria; Variedades riemanianas; Superficies algebricas
• Link de acesso: http://hdl.handle.net/1843/EABA-9GXNT3

The classic Bernstein theorem says that, if a function u : R2 ! R is anentire solution to the minimal surface equationdiv ru p1 + jruj2!= 0then u is a linear function, that is, the graph of u is necessarily a plan. Ifwe consider u : Rn1 ! R, a version of this theorem remains valid untiln 8, counter-examples were found in higher dimensions. Our main goal in this work is to show that this theorem is true for n 6. We will also show that if a hypersurface in the euclidean space is complete, minimal, stable and parabolic then it is necessarily a plan.