60 citations · 120 across the 20 of their papers we have counts for
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Blaschke--Santaló inequalities with respect to costs
Alexander V. Kolesnikov, Galyna V. Livshyts, Liran Rotem
We study functional Blaschke--Santaló inequalities in which the inner product is replaced by a cost. An inequality on each orthant, combined with Steiner symmetrization, gives a su…
On the functional Minkowski problem
Tomer Falah, Liran Rotem
To every log-concave function one may associate a pair of measures which are the surface area measures of . These are a functional extension of the classical…
The Complex Illumination Problem
Liran Rotem, Alon Schejter, Boaz A. Slomka
We formulate a complex analog of the celebrated Levi-Hadwiger-Boltyanski illumination (or covering) conjecture for complex convex bodies in C^n, as well as its (non-comparable) fra…
New Brunn--Minkowski and functional inequalities via convexity of entropy
Gautam Aishwarya, Liran Rotem
We study the connection between the concavity properties of a measure and the convexity properties of the associated relative entropy along optimal transport…
Stability and the equality case in the B-theorem
Orli Herscovici, Galyna V. Livshyts, Liran Rotem +1
In this paper, we show the stability, and characterize the equality cases in the strong B-inequality of Cordero-Erasquin, Fradelizi and Maurey \cite{B-conj}. As an application, we…
The anisotropic total variation and surface area measures
Liran Rotem
We prove a a formula for the first variation of the integral of a log-concave function, which allows us to define the surface area measure of such a function. The formula holds in…