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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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