Sobolev Inequalities, Riesz Transforms, and the Ricci Flow

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...

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Veröffentlicht in:Communications in mathematics and statistics 2014-06, Vol.2 (2), p.187-209
1. Verfasser: Ye, Rugang
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:2194-6701
2194-671X
DOI:10.1007/s40304-014-0035-9