Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms
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 subma...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-08-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02838-5 |
| _version_ | 1811345234387271680 |
|---|---|
| author | Yanlin Li Fatemah Mofarreh Ravi P. Agrawal Akram Ali |
| author_facet | Yanlin Li Fatemah Mofarreh Ravi P. Agrawal Akram Ali |
| author_sort | Yanlin Li |
| collection | DOAJ |
| description | 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 $\epsilon =1$ and Φ = 2 $\Phi =2$ . |
| first_indexed | 2024-04-13T20:00:02Z |
| format | Article |
| id | doaj.art-1eea1988e6d044748a2a4ebde35f39e2 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T20:00:02Z |
| publishDate | 2022-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-1eea1988e6d044748a2a4ebde35f39e22022-12-22T02:32:14ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-08-012022111710.1186/s13660-022-02838-5Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space formsYanlin Li0Fatemah Mofarreh1Ravi P. Agrawal2Akram Ali3Department of Mathematics, Hangzhou Normal UniversityMathematical Science Department Faculty of Science, Princess Nourah bint Abdulrahman UniversityDepartment of Mathematics, Texas A and M University-KingsvilleDepartment of Mathematics, College of Sciences, King Khalid UniversityAbstract 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 $\epsilon =1$ and Φ = 2 $\Phi =2$ .https://doi.org/10.1186/s13660-022-02838-5Reilly-type inequalityΦ-LaplacianEigenvalues estimatesSemislant submanifoldsSasakian space forms |
| spellingShingle | Yanlin Li Fatemah Mofarreh Ravi P. Agrawal Akram Ali Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms Journal of Inequalities and Applications Reilly-type inequality Φ-Laplacian Eigenvalues estimates Semislant submanifolds Sasakian space forms |
| title | Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms |
| title_full | Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms |
| title_fullStr | Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms |
| title_full_unstemmed | Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms |
| title_short | Reilly-type inequality for the Φ-Laplace operator on semislant submanifolds of Sasakian space forms |
| title_sort | reilly type inequality for the φ laplace operator on semislant submanifolds of sasakian space forms |
| topic | Reilly-type inequality Φ-Laplacian Eigenvalues estimates Semislant submanifolds Sasakian space forms |
| url | https://doi.org/10.1186/s13660-022-02838-5 |
| work_keys_str_mv | AT yanlinli reillytypeinequalityforthephlaplaceoperatoronsemislantsubmanifoldsofsasakianspaceforms AT fatemahmofarreh reillytypeinequalityforthephlaplaceoperatoronsemislantsubmanifoldsofsasakianspaceforms AT ravipagrawal reillytypeinequalityforthephlaplaceoperatoronsemislantsubmanifoldsofsasakianspaceforms AT akramali reillytypeinequalityforthephlaplaceoperatoronsemislantsubmanifoldsofsasakianspaceforms |