E104-06 - Forschungsbereich Konvexe und Diskrete Geometrie
-
Journal:
Journal of Differential Geometry
-
ISSN:
0022-040X
-
Date (published):
Mar-2025
-
Number of Pages:
30
-
Publisher:
INT PRESS BOSTON, INC
-
Peer reviewed:
Yes
-
Keywords:
fractional perimeter; projection body; radial mean body; fractional Sobolev inequality
-
Abstract:
Sharp affine fractional Sobolev inequalities for functions on R<sup>n</sup> are established. For each 0 < s < 1, the new inequalities are significantly stronger than (and directly imply) the sharp fractional Sobolev inequalities of Almgren and Lieb. In the limit as s → 1<sup>−</sup>, the new inequalities imply the sharp affine Sobolev inequality of Gaoyong Zhang. As a consequence, fractional Petty projection inequalities are obtained which are stronger than the fractional Euclidean isoperimetric inequalities, and a natural conjecture for radial mean bodies is proved.
en
Project title:
Bewertungen auf konvexen Funktionen: P 34446-N (FWF - Österr. Wissenschaftsfonds)
