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

Shahroud Azami

doi:10.4134/CKMS.c180006

Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

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Commun. Korean Math. Soc. 2019; 34(1): 287-301

Online first article June 18, 2018 Printed January 31, 2019

https://doi.org/10.4134/CKMS.c180006

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

Shahroud Azami

Imam Khomeini International University

Abstract

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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.

Keywords: Laplace, Ricci-Bourguignon flow, eigenvalue

MSC numbers: 58C40, 53C44, 53C21