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

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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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

Information

Published: March 2020
First available in Project Euclid: 16 March 2020

zbMATH: 07196513
MathSciNet: MR4077208
Digital Object Identifier: 10.2996/kmj/1584345691

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 1 • March 2020
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