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Entropy Functionals, Sobolev Inequalities and kappa-Noncollapsing Estimates along the Ricci Flow

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arxiv 0709.2724 v1 pith:WK7AIJCY submitted 2007-09-18 math.DG

Rugang Ye This is my paper · ORCID
classification math.DG
keywords entropyflowriccisobolevalongestimatesinequalitieskappa-noncollapsing
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In this survey we review Hamilton's entropy and Perelman's entropy, and provide motivations for these concepts. Then we review recent results on the logarithmic Sobolev inequality, the Sobolev inequalities and kappa-noncollapsing estimates along the Ricci flow, including the Ricci flow with surgeries.

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  1. Analytic Bertini theorem II --- The local case

    math.AG 2026-07 accept novelty 8.0 of 10

    The local analytic Bertini theorem holds: multiplier ideal sheaves of psh functions on polydisc products restrict to fibers outside a pluripolar set.

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