Sobolev Inequalities, Riesz Transforms and the Ricci Flow

Details Sobolev Inequalities, Riesz Transforms and the Ricci Flow Sobolev Inequalities, Riesz Transforms and the Ricci Flow

2007-09-04

arxiv.org/abs/0709.0512v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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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