A. Zvavitch

activity

20042026

most citedA remark on the Mahler conjecture: local minimality of the unit cube

60 citations · 154 across the 30 of their papers we have counts for

collaborators

Showing 2019Show all

5 papers · 1 filter

math.FA2019

Measure comparison and distance inequalities for convex bodies

Alexander Koldobsky, Grigoris Paouris, Artem Zvavitch

We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We al…

math.MG2019

Brunn-Minkowski type inequalities for the lattice point enumerator

David Iglesias, Jesús Yepes Nicolás, Artem Zvavitch

Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator $G_{n} (\cdot)$ are provided. In particular, we show that $$\mathrm{G}_n((1-λ)K +…

math.MG2019

Geometry and volume product of finite dimensional Lipschitz-free spaces

Matthew Alexander, Matthieu Fradelizi, Luis C. García-Lirola +1

The goal of this paper is to study geometric and extremal properties of the convex body $B_{F (M)}$ , which is the unit ball of the Lipschitz-free Banach space associated wi…

math.MG2019

Volume of the Minkowski sums of star-shaped sets

Matthieu Fradelizi, Zsolt Lángi, Artem Zvavitch

For a compact set $A \subset R^{d}$ and an integer $k \geq 1$ , let us denote by $A [k] = {a_{1} + \dots + a_{k} : a_{1}, \dots, a_{k} \in A} = i = 1 \sum k A$ the Minkowski…

math.MG2019★ 1 cited

Equipartitions and Mahler volumes of symmetric convex bodies

Matthieu Fradelizi, Alfredo Hubard, Mathieu Meyer +2

Following ideas of Iriyeh and Shibata we give a short proof of the three-dimensional Mahler conjecture {\mf for symmetric convex bodies}. Our contributions include, in particular,…