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.
Citation
Ha Tuan Dung. "Monotonicity of eigenvalues of the $p$-Laplace operator under the Ricci-Bourguignon flow." Kodai Math. J. 43 (1) 143 - 161, March 2020. https://doi.org/10.2996/kmj/1584345691