42 citations · 79 across the 18 of their papers we have counts for
4 papers · 1 filter
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…
Borell's generalized Prékopa-Leindler inequality: A simple proof
Arnaud Marsiglietti
We present a simple proof of Christer Borell's general inequality in the Brunn-Minkowski theory. We then discuss applications of Borell's inequality to the log-Brunn-Minkowski ineq…
A note on the convex infimum convolution inequality
Naomi Feldheim, Arnaud Marsiglietti, Piotr Nayar +1
We characterize the symmetric measures which satisfy the one dimensional convex infimum convolution inequality of Maurey. For these measures the tensorization argument yields the t…
On the Brunn-Minkowski inequality for general measures with applications to new isoperimetric-type inequalities
Galyna Livshyts, Arnaud Marsiglietti, Piotr Nayar +1
In this paper we present new versions of the classical Brunn-Minkowski inequality for different classes of measures and sets. We show that the inequality \[ μ(λA + (1-λ)B)^{1/n} \g…