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

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 in a simply connected Sasakian space form 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 , for a constant curvature and p = 2.

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