60 citations · 120 across the 20 of their papers we have counts for
9 papers · 1 filter
On p-Brunn-Minkowski and Brascamp-Lieb inequalities
Alexander V. Kolesnikov, Galyna Livshyts, Liran Rotem
We show that a strong version of the Brascamp--Lieb inequality for symmetric log-concave measure with -homogeneous potential is equivalent to a -Brunn--Minkowski inequali…
On weighted Blaschke--Santalo and strong Brascamp--Lieb inequalities
Andrea Colesanti, Alexander Kolesnikov, Galyna Livshyts +1
In this paper, we study new extensions of the functional Blaschke-Santaló inequalities, and explore applications of such new inequalities beyond the classical setting of the standa…
A Riesz representation theorem for log-concave functions
Liran Rotem
The classic Riesz representation theorem characterizes all linear and increasing functionals on the space of continuous compactly supported functions. A geometric versio…
Novel view on classical convexity theory
Vitali Milman, Liran Rotem
Let denote the Euclidean ball with diameter , i.e. with with center at and radius . We call such a bal…
Complemented Brunn-Minkowski Inequalities and Isoperimetry for Homogeneous and Non-Homogeneous Measures
Emanuel Milman, Liran Rotem
Elementary proofs of sharp isoperimetric inequalities on a normed space equipped with a measure so that is homogeneous are provided, a…
α-concave functions and a functional extension of mixed volumes
Vitali Milman, Liran Rotem
Mixed volumes, which are the polarization of volume with respect to the Minkowski addition, are fundamental objects in convexity. In this note we announce the construction of mixed…