42 citations · 79 across the 18 of their papers we have counts for
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The convexification effect of Minkowski summation
Matthieu Fradelizi, Mokshay Madiman, Arnaud Marsiglietti +1
Let us define for a compact set the sequence $$ A(k) = \left\{\frac{a_1+\cdots +a_k}{k}: a_1, \ldots, a_k\in A\right\}=\frac{1}{k}\Big(\underset{k\ {\rm ti…
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 an -Brunn-Minkowski inequality for convex measures in the unconditional case
Arnaud Marsiglietti
We consider a different -Minkowski combination of compact sets in than the one introduced by Firey and we prove an -Brunn-Minkowski inequality, $p \in [0,1…
On the improvement of concavity of convex measures
Arnaud Marsiglietti
We prove that a general class of measures, which includes -concave measures, is -concave according to the terminology of Borell, with additional assumptions on t…
Concavity properties of extensions of the parallel volume
Arnaud Marsiglietti
In this paper we establish concavity properties of two extensions of the classical notion of the outer parallel volume. On the one hand, we replace the Lebesgue measure by more gen…
On the analogue of the concavity of entropy power in the Brunn-Minkowski theory
Matthieu Fradelizi, Arnaud Marsiglietti
Elaborating on the similarity between the entropy power inequality and the Brunn-Minkowski inequality, Costa and Cover conjectured in {\it On the similarity of the entropy power in…