The first nonzero eigenvalue of the weighted p-Laplacian on differential forms

Abstract

We introduce the weighted p-Laplace operator acting on differential forms on a metric measure space, which is a natural generalization of the p-Laplace operator defined by Seto [32]. We obtain some sharp lower bounds of the first nonzero eigenvalue for the weighted p-Laplacian. Our results extend an estimate of Seto [32], as well as the eigenvalue estimates derived by Cui-Sun [8] for closed submanifolds.