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Monotonicity of
eigenvalues of geometric operators along the
Ricci–Bourguignon flow
Bin Chen, Qun He and Fanqi Zeng |
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Vol. 296 (2018), No. 1, 1–20
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Abstract |
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We study monotonicity of eigenvalues of the Schrödinger-type operator , where is a constant, along the Ricci–Bourguignon flow. For , we derive monotonicity of the lowest eigenvalue of the Schrödinger-type operator , which generalizes some results of Cao (2008). As an application, we rule out nontrivial compact steady breathers in the Ricci–Bourguignon flow. For , 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
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Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 53C44
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Milestones
Received: 23 January 2016
Revised: 7 March 2017
Accepted: 2 March 2018
Published: 1 May 2018
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Authors |
| Bin Chen | |
| School of Mathematical
Sciences Tongji University Shanghai China |
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| Qun He | |
| School of Mathematical
Sciences Tongji University Shanghai China |
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| Fanqi Zeng | |
| School of Mathematical
Sciences Tongji University Shanghai China |
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