Sobolev Inequalities, Riesz Transforms, and the Ricci Flow

Abstract

A number of results about deriving further Sobolev inequalities from a given Sobolev inequality are presented. Various techniques are employed, including Bessel potentials and Riesz transforms. Combining these results with the $$W^{1,2}$$ Sobolev inequality along the Ricci flow established by the author in earlier papers then yields various new Sobolev inequalities along the Ricci flow.