60 citations · 154 across the 30 of their papers we have counts for
7 papers · 1 filter
Distribution functions of sections and projections of convex bodies
Jaegil Kim, Vladyslav Yaskin, Artem Zvavitch
Typically, when we are given the section (or projection) function of a convex body, it means that in each direction we know the size of the central section (or projection) perpendi…
Characterization of Simplices via the Bezout Inequality for Mixed volumes
Christos Saroglou, Ivan Soprunov, Artem Zvavitch
We consider the following Bezout inequality for mixed volumes: It was shown…
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 : $$ A(k) = \left\{\frac{a_1+\cdots +a_k}{k} : a_1, \ldots, a_k\in A\right\}=\frac{1}{k}\Big…
Iterations of the projection body operator and a remark on Petty's conjectured projection inequality
Christos Saroglou, Artem Zvavitch
We prove that if a convex body has absolutely continuous surface area measure, whose density is sufficiently close to the constant, then the sequence of convex bodies co…
A discrete version of Koldobsky's slicing inequality
Matthew Alexander, Martin Henk, Artem Zvavitch
Let be a number of integer lattice points contained in a set . In this paper we prove that for each there exists a constant depending on onl…
Bezout Inequality for Mixed volumes
Ivan Soprunov, Artem Zvavitch
In this paper we consider the following analog of Bezout inequality for mixed volumes: $$V(P_1,\dots,P_r,Δ^{n-r})V_n(Δ)^{r-1}\leq \prod_{i=1}^r V(P_i,Δ^{n-1})\ \text{ for }2\leq r\…
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…