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Eigenvalues and
entropies under the harmonic-Ricci flow
Yi Li |
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Vol. 267 (2014), No. 1, 141–184
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Abstract |
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In this paper, the author discusses the eigenvalues and entropies under the harmonic-Ricci flow, which is the Ricci flow coupled with the harmonic map flow. We give an alternative proof of results for compact steady and expanding harmonic-Ricci breathers. In the second part, we derive some monotonicity formulas for eigenvalues of the Laplacian under the harmonic-Ricci flow. Finally, we obtain the first variation of the shrinker and expanding entropies of the harmonic-Ricci flow. |
Keywords
Eigenvalue, entropies, harmonic-Ricci flow, harmonic-Ricci
breathers
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Mathematical Subject Classification 2010
Primary: 53C44, 35K55
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Milestones
Received: 27 August 2012
Revised: 6 January 2013
Accepted: 16 January 2013
Published: 22 December 2013
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Authors |
| Yi Li | |
| Department of Mathematics Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218 United States |
Department of Mathematics Shanghai Jiao Tong University 800 Dong Chuan Road, Min Hang District Shanghai, 200240 China |
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