Maximizando o primeiro autovalor do operador de Jacobi
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...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Institución: | Universidade Federal do Ceará (UFC) |
| Repositorio: | Repositório Institucional da Universidade Federal do Ceará (UFC) |
| Idioma: | portugués |
| OAI Identifier: | oai:repositorio.ufc.br:riufc/72438 |
| Acceso en línea: | http://www.repositorio.ufc.br/handle/riufc/72438 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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