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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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