Abolarinwa, A. and Edeki, S.O. and Ehigie, J. O (2020) On the spectrum of the weighted p-Laplacian under the Ricci-harmonic flow. Journal of Inequalities and Application.
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Abstract
This paper studies the behaviour of the spectrum of the weighted p-Laplacian on a complete Riemannian manifold evolving by the Ricci-harmonic flow. Precisely, the first eigenvalue diverges in a finite time along this flow. It is further shown that the same divergence result holds on gradient shrinking and steady almost Ricci-harmonic solitons under the condition that the soliton function is nonnegative and superharmonic. We also continue the program in (Abolarinwa, Adebimpe and Bakare in J. Ineq. Appl. 2019:10, 2019) to the case of volume-preserving Ricci-harmonic flow.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Ricci harmonic flow; Laplace–Beltrami operator; Eigenvalue; Monotonicity; Ricci solitons |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |
| Depositing User: | Mrs Patricia Nwokealisi |
| Date Deposited: | 27 May 2022 12:47 |
| Last Modified: | 27 May 2022 12:47 |
| URI: | http://eprints.covenantuniversity.edu.ng/id/eprint/15894 |
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