Curvatura gaussiana prescrita em superfícies com característica de Euler negativa
This dissertation aims to study the problem of prescribing the Gaussian curvature on closed Riemannian surfaces with negative Euler characteristic, detailing the results obtained in [3]. The work investigates the existence of multiple solutions to the problem of finding conformal Riemannian metrics...
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| Tipo de recurso: | tesis de maestría |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | Brasil |
| Institución: | Universidade Federal de Sergipe (UFS) |
| Repositorio: | Repositório Institucional da UFS |
| Idioma: | portugués |
| OAI Identifier: | oai:oai:ri.ufs.br:repo_01:riufs/20459 |
| Acceso en línea: | https://ri.ufs.br/jspui/handle/riufs/20459 |
| Access Level: | acceso abierto |
| Palabra clave: | Processos gaussianos Curvatura Curvatura gaussiana Curvas em superfícies Passo da Montanha Métricas conformes Gaussian processes Curvature Gaussian curvature Curves on surfaces Mountain pass Conformal metrics CIENCIAS EXATAS E DA TERRA::MATEMATICA |
| Sumario: | This dissertation aims to study the problem of prescribing the Gaussian curvature on closed Riemannian surfaces with negative Euler characteristic, detailing the results obtained in [3]. The work investigates the existence of multiple solutions to the problem of finding conformal Riemannian metrics whose Gaussian curvature equals a given function. Under certain conditions, the problem admits a unique solution, which corresponds to the global minimum of a specific functional. By considering small perturbations to a parameter of the function intended to be prescribed as the Gaussian curvature, it is shown that the functional admits an additional critical point of the “mountain pass” type. Furthermore, the behavior of this second solution is investigated as the parameter approaches zero. |
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