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Sharp logarithmic
Sobolev inequalities along an extended Ricci flow and
applications
Guoqiang Wu and Yu Zheng |
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Vol. 298 (2019), No. 2, 483–509
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Abstract |
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We prove a sharp Logarithmic Sobolev inequality along an extended Ricci flow. As applications, we derive an integral bound for the conjugate heat kernel and also obtain Lipschitz continuity of the pointed Nash entropy. Finally, based on these results, we prove an -regularity theorem for this extended Ricci flow. |
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Keywords
conjugate heat kernel, logarithmic Sobolev inequalities,
$\varepsilon$-regularity.
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Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 53C21
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Milestones
Received: 20 January 2018
Revised: 15 May 2018
Accepted: 24 June 2018
Published: 8 March 2019
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Authors |
| Guoqiang Wu | |
| School of Science Zhejiang Sci-Tech University Hangzhou China |
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| Yu Zheng | |
| School of Mathematical
Sciences East China Normal University Shanghai China |
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