Communications of the Korean Mathematical Society (대한수학회논문집)

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EIGENVALUE MONOTONICITY OF (p, q)-LAPLACIAN ALONG THE RICCI-BOURGUIGNON FLOW

  • Azami, Shahroud (Department of Mathematics Faculty of Sciences Imam Khomeini International University)
  • Received : 2018.01.07
  • Accepted : 2018.04.25
  • Published : 2019.01.31
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Abstract

In this paper we study monotonicity the first eigenvalue for a class of (p, q)-Laplace operator acting on the space of functions on a closed Riemannian manifold. We find the first variation formula for the first eigenvalue of a class of (p, q)-Laplacians on a closed Riemannian manifold evolving by the Ricci-Bourguignon flow and show that the first eigenvalue on a closed Riemannian manifold along the Ricci-Bourguignon flow is increasing provided some conditions. At the end of paper, we find some applications in 2-dimensional and 3-dimensional manifolds.

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References

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