A Reverse Rogers–Shephard Inequality for Log-Concave Functions

We will prove a reverse Rogers–Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of ℓ p -diferences of convex bodies under the condition that their pola...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	The Journal of Geometric Analysis 2019-01, Vol.29 (1), p.299-315
1. Verfasser:	Alonso-Gutiérrez, David
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstract Harmonic Analysis Convex and Discrete Geometry Differential Geometry Dynamical Systems and Ergodic Theory Equality Fourier Analysis Geometry Global Analysis and Analysis on Manifolds Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	We will prove a reverse Rogers–Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of ℓ p -diferences of convex bodies under the condition that their polar bodies have opposite barycenters.
ISSN:	1050-6926 1559-002X
DOI:	10.1007/s12220-018-9991-8