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AIMS Mathematics

2017, Volume 2, Issue 2: 230-243. doi: 10.3934/Math.2017.2.230
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Research article

Monotonicity of eigenvalues of Witten-Laplace operator along the Ricci-Bourguignon flow

  • Department of Mathematics, Faculty of Sciences, Imam Khomeini International University, Qazvin, Iran
  • Received: 11 February 2017 Accepted: 28 March 2017 Published: 13 April 2017

  • In this article we will investigate monotonicity for the first eigenvalue problem of the Witten-Laplace operator acting on the space of functions along the Ricci-Bourguignon flow on closed manifolds. We find the first variation formula for the eigenvalues of Witten-Laplacian on a closed manifold evolving by the Ricci-Bourguignoni flow and construct various monotonic quantities. At the end we find some applications in 2-dimensional and 3-dimensional manifolds and give an example.

    Citation: Shahroud Azami. Monotonicity of eigenvalues of Witten-Laplace operator along the Ricci-Bourguignon flow[J]. AIMS Mathematics, 2017, 2(2): 230-243. doi: 10.3934/Math.2017.2.230

    Related Papers:

  • In this article we will investigate monotonicity for the first eigenvalue problem of the Witten-Laplace operator acting on the space of functions along the Ricci-Bourguignon flow on closed manifolds. We find the first variation formula for the eigenvalues of Witten-Laplacian on a closed manifold evolving by the Ricci-Bourguignoni flow and construct various monotonic quantities. At the end we find some applications in 2-dimensional and 3-dimensional manifolds and give an example.


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  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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