Functional versions of Lp-affine surface area and entropy inequalities
Caglar, Umut; Fradelizi, Matthieu; Guédon, Olivier; Lehec, Joseph; Schütt, Carsten; Werner, Elisabeth (2016), Functional versions of Lp-affine surface area and entropy inequalities, International Mathematics Research Notices, 2016, 4, p. 1223-1250. 10.1093/imrn/rnv151
Type
Article accepté pour publication ou publiéDate
2016Journal name
International Mathematics Research NoticesVolume
2016Number
4Publisher
Duke University Press
Published in
Paris
Pages
1223-1250
Publication identifier
Metadata
Show full item recordAuthor(s)
Caglar, UmutFradelizi, Matthieu
Guédon, Olivier
Lehec, Joseph

Schütt, Carsten
Werner, Elisabeth
Abstract (EN)
In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowskitheory is a modern analogue of the classical Brunn Minkowski theory. A cornerstoneof this theory is the Lp-affine surface area for convex bodies. Here, we introducea functional form of this concept, for log concave and s-concave functions. Weshow that the new functional form is a generalization of the original Lp-affinesurface area. We prove duality relations and affine isoperimetric inequalities for logconcave and s-concave functions. This leads to a new inverse log-Sobolevinequality for s-concave densitiesSubjects / Keywords
affine isoperimetric inequalities; entropy; log- Sobolev inequalitiesRelated items
Showing items related by title and author.
-
Lehec, Joseph (2013) Article accepté pour publication ou publié
-
Eldan, Ronen; Lee, James; Lehec, Joseph (2017) Chapitre d'ouvrage
-
Chafaï, Djalil; Lehec, Joseph (2020) Chapitre d'ouvrage
-
Schlichting, André; Menz, Georg; Léonard, Christian; Lehec, Joseph; Gozlan, Nathael; Boissard, Emmanuel (2014) Communication / Conférence
-
Dolbeault, Jean (2021) Article accepté pour publication ou publié