Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 2
149
Views
11
CrossRef citations to date
0
Altmetric
Articles

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

ORCID Icon, , &
Pages 702-713 | Received 20 May 2019, Accepted 11 Apr 2020, Published online: 05 May 2020
 

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 Σn in a simply connected Sasakian space form M~2m+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 S2m+1, for a constant curvature κ=1 and p = 2.

2010 Mathematics Subject Classifications:

Acknowledgments

The authors would like to express their gratitude to Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing funding research groups under the research grant number R. G. P. 2/71/41. Akram Ali would like to thank to the Departamento de Matematica, Universidade Federal do Ceara, Brazil, where a part of this work was carried out. He is grateful to Professors Ernani Ribeiro Jr, for the warm hospitality and their constant encouragement.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors would like to express their gratitude to Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing funding research groups under the research grant number R. G. P. 2/71/41.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.