Eigenvalue inequalities for the p-Laplacian operator on C-totally real submanifolds in Sasakian space forms,Applicable Analysis

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Eigenvalue inequalities for the p-Laplacian operator on C-totally real submanifolds in Sasakian space forms
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-05-05 , DOI: 10.1080/00036811.2020.1758307
Akram Ali _{1,

2} , Ali H. Alkhaldi ₁ , Pişcoran Laurian-Ioan ₃ , Rifaqat Ali ₄

Affiliation

ABSTRACT

The main objective of this paper is to provide various estimates of the first eigenvalue of the p-Laplacian operator on a closed oriented n-dimensional C-totally real submanifold $Σ^{n}$ in a simply connected Sasakian space form ${\tilde{M}}^{2 m + 1} (κ)$ with a constant ϕ-sectional curvature κ. As applications, we generalize the Reilly-type inequality for the Laplacian [Chen and Wei. Reilly-type inequalities for p-Laplacian on submanifolds in space forms. Nonlinear Anal. 2019;84:210–217; Du and Mao. Reilly-type inequalities for p-Laplacian on compact Riemannian manifolds. Front Math China. 2015;10(3):583–594] to the p-Laplacian for C-totally real submanifold in a sphere $S^{2 m + 1}$ , for a constant curvature $κ = 1$ and p = 2.

更新日期：2020-05-05

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