Functional Versions of Lp-Affine Surface Area and Entropy Inequalities
| Autor: | Matthieu Fradelizi, Umut Caglar, Elisabeth M. Werner, Carsten Schütt, Olivier Guédon, Joseph Lehec |
|---|---|
| Přispěvatelé: | Case Western Reserve University [Cleveland], Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Mathematisches Seminar [Kiel], Christian-Albrechts-Universität zu Kiel (CAU), ANR-11-BS01-0007,GeMeCoD,Géométrie des mesures convexes et discrètes(2011), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Convex geometry Inequality Entropy (statistical thermodynamics) General Mathematics media_common.quotation_subject 010102 general mathematics Mathematical analysis Regular polygon Inverse [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences 010101 applied mathematics Mathematics::Metric Geometry Affine transformation 0101 mathematics Isoperimetric inequality Mathematics media_common |
| Zdroj: | International Mathematics Research Notices International Mathematics Research Notices, Oxford University Press (OUP), 2016, pp.1223-1250. ⟨10.1093/imrn/rnv151⟩ |
| ISSN: | 1073-7928 1687-0247 |
| DOI: | 10.1093/imrn/rnv151⟩ |
| Popis: | International audience; In contemporary convex geometry, the rapidly developing Lp-Brunn-Minkowski theory is a modern analogue of the classical Brunn-Minkowski theory. A central notion of this theory is the Lp-affine surface area of convex bodies. Here, we introduce a functional analogue of this concept, for log-concave and s-concave functions. We show that the new analytic notion is a generalization of the original Lp-affine surface area. We prove duality relations and affine isoperimetric inequalities for log-concave and s-concave functions. This leads to a new inverse log-Sobolev inequality for s-concave densities. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|