Estimativas universais para autovalores de operadores na forma divergente em variedades Riemannianas isometricamente imersas no espaço Euclidiano

Abstract

The focus of this work is the study of the Dirichlet eigenvalue problem for the (η, T)-divergent operator, L, in a bounded domain of a complete Riemannian manifold, isometrically immersed in Euclidean space . We obtained estimates of universal inequalities of eigenvalues as a function of their order and the first eigenvalue. As an application we obtained the estimate of the gap between consecutive eigenvalues, also in terms of the order and the first eigenvalue for the Euclidean case, and if M is a pinched Cartan-Hadamard Manifold, we obtained the estimate of gap in particular cases of the L operator