Some results of evolution of the first eigenvalue of weighted $p$-Laplacian along the extended Ricci flow
Commun. Korean Math. Soc.
Published online June 16, 2020
Shahroud azami
Imam Khomeini International University
Abstract : 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.
Keywords : Laplace, Ricci flow, eigenvalue
MSC numbers : 58C40; 53C44, 53C21
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