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Abstract
The problem of geometric flow and determining the eigenvalues for nonlinear operators acting on finite-dimensional manifolds is a known problem. In this paper we will consider the eigenvalue problem for the p-Laplace operator acting on the space of functions on closed manifolds. We find the first variation formula for the eigenvalues of p-Laplacian on a closed manifold evolving by the Yamabe flow and find some applications.
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1 Faculty of Sciences, Department of Mathematics, Imam Khomeini International University, Qazvin, Iran