Upper Bounds for the First Eigenvalue of a Jacobi Type Operator Via Anisotropic Mean Curvatures

Our purpose in this article is to obtain sharp upper estimates for the first positive eigenvalue of a Jacobi type operator, which is a suitable extension of the linearized operators of the higher order mean curvatures of a closed hypersurface immersed in the Euclidean space, through its anisotropic mean curvatures.