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http://dx.doi.org/10.4134/CKMS.c190353

SOME RESULTS OF EVOLUTION OF THE FIRST EIGENVALUE OF WEIGHTED p-LAPLACIAN ALONG THE EXTENDED RICCI FLOW  

Azami, Shahroud (Department of Pure Mathematics Faculty of Science Imam Khomeini International University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.3, 2020 , pp. 953-966 More about this Journal
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; extended Ricci flow; eigenvalue;
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