Eigenvalue inequalities for the p-Laplacian operator on C-totally real submanifolds in Sasakian space forms. Issue 2 (22nd January 2022) - Ali, Akram; Alkhaldi, Ali H.; Laurian-Ioan, Pişcoran; Ali, Rifaqat
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 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.