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In this article we study the evolution and monotonicity of the first non-zero eigenvalue of weighted $p$-Laplacian operator which it acting on the space of functions on closed oriented Riemannian $n$-manifolds along the extended Ricci flow and normalized extended Ricci flow. We show that the first eigenvalue of weighted $p$-Laplacian operator diverges as $t$ approaches to maximal existence time. Also, we obtain evolution formulas of the first eigenvalue of weighted $p$-Laplacian operator along the normalized extended Ricci flow and using it we find some monotone quantities along the normalized extended Ricci flow under the certain geometric conditions.
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참고문헌 (20)
참고문헌 신청
A. Abolarinwa / 2015 / Evolution and monotonicity of the first eigenvalue of p-Laplacian under the Ricci-harmonic flow / J. Appl. Anal 21(2):147~160
A. Abolarinwa / 2019 / Eigenvalues of the weighted Laplacian under the extended Ricci flow / Adv. Geom 19(1):131~143
A. Abolarinwa / 2019 / Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow / J. Inequal. Appl 2019:10~25
S. Azami / 2016 / Eigenvalues variation of the p-Laplacian under the Yamabe flow / Cogent Math 3:1236566~1236575
S. Azami / 2017 / Monotonicity of eigenvalues of Witten-Laplace operator along the RicciBourguignon flow / AIMS Math 2(2):230~243
A. Abolarinwa / 2019 / Eigenvalues of the weighted Laplacian under the extended Ricci flow / Adv. Geom 19(1):131~143
A. Abolarinwa / 2019 / Monotonicity formulas for the first eigenvalue of the weighted p-Laplacian under the Ricci-harmonic flow / J. Inequal. Appl 2019:10~25
S. Azami / 2016 / Eigenvalues variation of the p-Laplacian under the Yamabe flow / Cogent Math 3:1236566~1236575
S. Azami / 2017 / Monotonicity of eigenvalues of Witten-Laplace operator along the RicciBourguignon flow / AIMS Math 2(2):230~243
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