154 citations · 1.3k across the 48 of their papers we have counts for
5 papers · 1 filter
Metric complexity is a Bryant--Tupper diversity
Gautam Aishwarya, Dongbin Li, Mokshay Madiman +1
The metric complexity (sometimes called Leinster--Cobbold maximum diversity) of a compact metric space is a recently introduced isometry-invariant of compact metric spaces which ge…
Weighted Brunn-Minkowski Theory I: On Weighted Surface Area Measures
Matthieu Fradelizi, Dylan Langharst, Mokshay Madiman +1
The Brunn-Minkowski theory in convex geometry concerns, among other things, the volumes, mixed volumes, and surface area measures of convex bodies. We study generalizations of thes…
On the volume of the Minkowski sum of zonoids
Matthieu Fradelizi, Mokshay Madiman, Mathieu Meyer +1
We explore some inequalities in convex geometry restricted to the class of zonoids. We show the equivalence, in the class of zonoids, between a local Alexandrov-Fenchel inequality,…
Sumset estimates in convex geometry
Matthieu Fradelizi, Mokshay Madiman, Artem Zvavitch
Sumset estimates, which provide bounds on the cardinality of sumsets of finite sets in a group, form an essential part of the toolkit of additive combinatorics. In recent years, pr…
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…