A Gage-type estimate for the $p$-fundamental tone and applications to submanifolds

A generalization of the classical Gage’s upper bound for the fundamental tone of the Laplacian on complete non-compact Riemannian manifolds to the $p$-Laplacian context is obtained. As an application, upper estimates for the $p$-fundamental tone of complete non-compact submanifolds of space forms with constant nonpositive sectional curvature, and for a class of product spaces, are presented.