Monotonicity of eigenvalues of geometric operators along the Ricci–Bourguignon flow

We study monotonicity of eigenvalues of the Schrödinger-type operator $- Δ + c R$ , where $c$ is a constant, along the Ricci–Bourguignon flow. For $c \neq 0$ , we derive monotonicity of the lowest eigenvalue of the Schrödinger-type operator $- Δ + c R$ , which generalizes some results of Cao (2008). As an application, we rule out nontrivial compact steady breathers in the Ricci–Bourguignon flow. For $c = 0$ , we derive monotonicity of the first eigenvalue of the Laplacian, which generalizes some results of Ma (2006).

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Keywords

eigenvalue, Laplacian, monotonicity, Ricci–Bourguignon flow, breathers

Mathematical Subject Classification 2010

Primary: 53C21

Secondary: 53C44

Milestones

Received: 23 January 2016

Revised: 7 March 2017

Accepted: 2 March 2018

Published: 1 May 2018

Authors

Bin Chen
School of Mathematical Sciences Tongji University Shanghai China

Qun He
School of Mathematical Sciences Tongji University Shanghai China

Fanqi Zeng
School of Mathematical Sciences Tongji University Shanghai China

Vol. 296, No. 1, 2018

Bin Chen, Qun He and Fanqi Zeng

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors