Sobolev Inequalities, Riesz Transforms and the Ricci Flow

2007/09/04 by Ye, Rugang
#53C20 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0709.0512

Abstract

In this paper we study the problem of deriving further Sobolev inequalities from a given Sobolev inequality. We use several different methods, including Bessel potentials and Riesz transforms. We apply the results to the Ricci flow to extend the author's results on the W^1,2 Sobolev inequality along the Ricci flow to W^1,p and W^2,p Sobolev inequalities for general p.

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