Eigenvalue monotonicity of $(p,q)$-Laplacian along the Ricci-Bourguignon flow
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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.
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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