Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2019.10.09
  • Accepted : 2020.05.22
  • Published : 2020.07.31
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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.

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References

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