Monotonicity of eigenvalues of the p-Laplace operator under the Ricci-Bourguignon flow

Abstract

Given a compact Riemannian manifold without boundary, in this paper, we discuss the monotonicity of the first eigenvalue of the p-Laplace operator under the Ricci-Bourguignon flow. We prove that the first eigenvalue of the p-Laplace operator is strictly monotone increasing and differentiable almost everywhere along the Ricci-Bourguignon flow under some different curvature assumptions. Moreover, we obtain various monotonicity quantities about the first eigenvalue of the p-Laplace operator along the Ricci-Bourguignon flow.