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math.MG2016★ 1 cited
On the stability of Brunn-Minkowski type inequalities
Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti
Log-Brunn-Minkowski inequality was conjectured by Boröczky, Lutwak, Yang and Zhang \cite{BLYZ}, and it states that a certain strengthening of the classical Brunn-Minkowski inequali…
math.MG2015★ 14 cited
Do Minkowski averages get progressively more convex?
Matthieu Fradelizi, Mokshay Madiman, Arnaud Marsiglietti +1
Let us define, for a compact set , the Minkowski averages of : $$ A(k) = \left\{\frac{a_1+\cdots +a_k}{k} : a_1, \ldots, a_k\in A\right\}=\frac{1}{k}\Big…