5 papers
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 transpo…
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 inequal…
Sectional curvature and matrix displacement convexity
Gautam Aishwarya, Liran Rotem, Yair Shenfeld
We show that the sectional curvature of a Riemannian manifold is nonnegative if, and only if, the entropy functional is matrix displacement convex. As an application we obtain intr…
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 classic…
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…