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Azami, Shahroud
IndoMS
Mathematics

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EIGENVALUES VARIATION OF THE P-LAPLACIAN UNDER THE RICCI FLOW ON SM Azami, Shahroud
Journal of the Indonesian Mathematical Society Volume 22 Number 2 (October 2016)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.22.2.215.157-177

Abstract

Let (M,F) be a compact Finsler manifold. Studying the eigenvalues and eigenfunctions for the linear and nonlinear geometric operators is a known problem. In this paper we will consider the eigenvalue problem for the p-laplace operator for Sasakian metric acting on the space of functions on SM. We find the first variation formula for the eigenvalues of p-Laplacian on SM evolving by the Ricci flow on M and give some examples.DOI : http://dx.doi.org/10.22342/jims.22.2.215.157-177
First Eigenvalues of Geometric Operator under The Ricci-Bourguignon Flow Azami, Shahroud
Journal of the Indonesian Mathematical Society Volume 24 Number 1 (April 2018)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.24.1.434.51-60

Abstract

Let $(M,g(t))$ be a compact Riemannian manifold  and  the metric $g(t)$ evolve by the Ricci-Bourguignon flow. We find the formula variation of the eigenvalues of  geometric operator $-\Delta_{\phi}+cR$ under  the Ricci-Bourguignon flow, where  $\Delta_{\phi}$  is the Witten-Laplacian operator and $R$ is the scalar curvature. In the final  we show that some quantities dependent to the eigenvalues of  the geometric operator are  nondecreasing along the Ricci-Bourguignon flow on  closed manifolds  with nonnegative curvature.
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