Vol. 296, No. 1, 2018

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ISSN: 0030-8730
Monotonicity of eigenvalues of geometric operators along the Ricci–Bourguignon flow

Bin Chen, Qun He and Fanqi Zeng

Vol. 296 (2018), No. 1, 1–20
Abstract

We study monotonicity of eigenvalues of the Schrödinger-type operator Δ + cR, where c is a constant, along the Ricci–Bourguignon flow. For c0, we derive monotonicity of the lowest eigenvalue of the Schrödinger-type operator Δ + cR, 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).

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