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

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

2007-09-18

arxiv.org/abs/0709.2724v1

Mathematics

Differential Geometry

This survey was written for the 4th International Congress of Chinese Mathematicians to be held in Hangzhou, China in December

Scientific paper

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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