2025-02-252025-02-252023-12-13SANTOS, Williams da Silva. A estimativa do primeiro autovalor do laplaciano para hipersuperfícies mínimas. Orientador: Adam Oliveira da Silva. 2023. 58 f. Trabalho de Conclusão de Curso (Licenciatura em Matemática) – Faculdade de Matemática, Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, Belém, 2023. Disponível em:. Acesso em:.https://bdm.ufpa.br/jspui/handle/prefix/7741In this work, we will address the main concepts of Riemannian geometry, which is a field of differential geometry dedicated to the study of Riemannian manifolds. These concepts have the capacity to extend, for example, the understanding of the main operators of integral differential calculus, such as the laplacian. We will use these concepts to obtain an estimate for the first eigenvalue of the Laplacian for minimally dipped hypersurfaces in Sn+1, which was obtained in [2], in this demonstration we employ the well-known Reilly formula. Finally, we will combine this result with a result obtained by P. Yang and S. T. Yau in [8], to obtain a lower bound for the area of a minimal hypersurface in terms of its genus, its dimension and the first eigenvalue of the laplacian..Acesso AbertoGeometriaGeometria riemannianaAutovalorLaplacianoGeometryRiemannian geometryEigenvalueLaplacianCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICATrabalho de Curso - Graduação - Monografia