Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms - Yanlin Li; Fatemah Mofarreh; Ravi P. Agrawal; Akram Ali (Journal of Inequalities and Applications, 2022)
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 $ε =1$ and Φ = 2 $Φ =2$ .