Reilly-type inequalities for [formula omitted]-Laplacian on submanifolds in space forms

Abstract

Let M be an n-dimensional closed orientable submanifold in an N-dimensional space form. When 1<p≤n2+1, we obtain an upper bound for the first nonzero eigenvalue of the p-Laplacian in terms of the mean curvature of M and the curvature of the space form. This generalizes the Reilly inequality for the Laplacian (Soufi and Ilias, 1992; Reilly, 1977) to the p-Laplacian and extends the work of Du and Mao (2015) for the p-Laplacian.