Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms

Abstract

This paper aims to establish new upper bounds for the first positive eigenvalue of the Φ-Laplacian operator on Riemannian manifolds in terms of mean curvature and constant sectional curvature. The first eigenvalue for the Φ-Laplacian operator on closed oriented m-dimensional semislant submanifolds in a Sasakian space form is estimated in various ways. Several Reilly-like inequalities are generalized from our findings for Laplacian to the Φ-Laplacian on semislant submanifolds in a sphere with epsilon =1 and Phi =2.