Estimativas de Gaps entre autovalores consecutivos do Laplaciano

Abstract

This work is based on the article Estimates of the Gaps Between Consecutive Eigenvalues of Laplacian by Daguang Chen, Tao Zheng and Hongcang Yang, in which were obtained estimates for the upper bound of the gap between consecutive eigenvalues for the eigenvalue problem of the Dirichlet Laplacian on a bounded domain in Euclidean space. Such estimates are the best possible in relation to the Weyl formula. Furthmore, a conjecture for the eigenvalue problem in a Riemannian manifold was proposed. The latter was motivaded by two examples, one in the context of a Hyperbolic space and the other in the context of simply connected complete noncompact Riemannian manifold with bounded negative sectional curvature.