4 citations · 8 across the 6 of their papers we have counts for
6 papers
Pinsker inequalities and related Monge-Ampère equations for log concave functions
Umut Caglar, Alexander V. Kolesnikov, Elisabeth M. Werner
In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant en…
Affine isoperimetric inequalities in the functional Orlicz-Brunn-Minkowski theory
Umut Caglar, Deping Ye
In this paper, we develop a basic theory of Orlicz affine and geominimal surface areas for convex and -concave functions. We prove some basic properties for these newly introduc…
Functional versions of L_p-affine surface area and entropy inequalities
U. Caglar, M. Fradelizi, O. Guedon +3
In contemporary convex geometry, the rapidly developing L_p-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the…
Mixed f-divergence and inequalities for log concave functions
Umut Caglar, Elisabeth M. Werner
Mixed -divergences, a concept from information theory and statistics, measure the difference between multiple pairs of distributions. We introduce them for log concave functions…
Stability results for some geometric inequalities and their functional versions
Elisabeth M. Werner, Umut Caglar
The Blaschke Santaló inequality and the affine isoperimetric inequalities are major inequalities in convex geometry and they have a wide range of applications. Functional ver…
Divergence for s-concave and log concave functions
Umut Caglar, Elisabeth M. Werner
We prove new entropy inequalities for log concave and s-concave functions that strengthen and generalize recently established reverse log Sobolev and Poincare inequalities for such…