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math.DG2025
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 tensor is matrix displacement convex. As an application, under the assumpt…
math.FA2025
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…
math.MG2025
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…