2012/10/16 by Liran Rotem, Rotem, Liran
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #Mathematical Inequalities and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1210.4340
openalex publication_date 2012/10/16 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
In this paper we extend some notions, previously defined for log-concave functions, to the larger domain of so-called α-concave functions. We begin with a detailed discussion of support functions - first for log-concave functions, and then for general α-concave functions. We continue by defining mean width, and proving some basic results such as an Urysohn type inequality. Finally, we demonstrate how such geometric results can imply Poincaré type inequalities.