期刊
INTERNATIONAL JOURNAL OF MATHEMATICS
卷 33, 期 2, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0129167X22500161
关键词
Reilly-type inequality; p-Laplacian; eigenvalue estimate; Lagrangian submanifolds
类别
资金
- Deanship of Scientific Research at King Khalid University, Saudi Arabia [R. G. P. 2/74/42]
- National Research Foundation of Korea (NRF) - Korea government (MSIT) [2020R1F1A1A01069289]
- National Research Foundation of Korea [2020R1F1A1A01069289] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
The goal of this paper is to prove new upper bounds for the first positive eigenvalue of the p-Laplacian operator in terms of the mean curvature and constant sectional curvature on Riemannian manifolds. In particular, we provide various estimates of the first eigenvalue of the p-Laplacian operator on closed orientate n-dimensional Lagrangian submanifolds in a complex space form M-n(4 epsilon) with constant holomorphic sectional curvature 4 epsilon. As applications of our main theorem, we generalize the Reilly-inequality for the Laplacian to the p-Laplacian for a Lagrangian submanifold in a complex Euclidean space and complex projective space for epsilon = 0 and epsilon = 1, respectively.
The goal of this paper is to prove new upper bounds for the first positive eigenvalue of the p-Laplacian operator in terms of the mean curvature and constant sectional curvature on Riemannian manifolds. In particular, we provide various estimates of the first eigenvalue of the p-Laplacian operator on closed orientate n-dimensional Lagrangian submanifolds in a complex space form M-n(4 epsilon) with constant holomorphic sectional curvature 4 epsilon. As applications of our main theorem, we generalize the Reilly-inequality for the Laplacian [R. C. Reilly, On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space, Comment. Math. Helv. 52(4) (1977) 525-533] to the p-Laplacian for a Lagrangian submanifold in a complex Euclidean space and complex projective space for epsilon = 0 and epsilon = 1, respectively.
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