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.
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