Maximizando o primeiro autovalor do operador de Jacobi

• Ano de defesa: 2022
• Autor(a) principal: Vasconcelos, Rosa Tayane de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Operador de Jacobi; Primeiro autovalor; Operador laplaciano; Operador de Schrödinger; Funcional de Willmore; Curvatura escalar total; Jacobi operator; First eigenvalue; Laplacian operator; Schrödinger operator; Willmore functional; Total scalar curvature
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/72438

We consider the Jacobi operator, defined on a closed oriented hypersurfaces immersed in the Euclidean space with the same volume of the unit sphere by L = −∆−|II|2, where −∆ is the Laplace-Beltrami operator with ∆u = div(∇u) and |II| 2 = ∑nj = 1k2j is the square of second fundamental form. We show a generalization for the classical result of the Willmore functional for the Euclidean sphere. As a consequence, by adding a topological hypothesis we prove that the fi rst eigenvalue of the Jacobi operator in the Euclidean sphere is a global maximum.