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

Abstract

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 M ˜ 2 k + 1 ( ϵ ) 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 S 2 n + 1 with ϵ = 1 $\epsilon =1$ and Φ = 2 $\Phi =2$ .

Keywords

• Reilly-type inequality
• Φ-Laplacian
• Eigenvalues estimates
• Semislant submanifolds
• Sasakian space forms