2 citations · 2 across the 9 of their papers we have counts for
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Simultaneous Busemann-Petty and Shephard Volume Comparisons
Artem Zvavitch
We study the simultaneous Busemann-Petty and Shephard volume comparison problem: whether comparison of the volumes of all central hyperplane sections and all orthogonal hyperplane…
Inequalities for the Radon transform on convex sets
Apostolos Giannopoulos, Alexander Koldobsky, Artem Zvavitch
Several years ago the authors started looking at some problems of convex geometry from a more general point of view, replacing volume by an arbitrary measure. This approach led to…
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 are provided. In particular, we show that $$\mathrm{G}_n((1-λ)K +…
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 , which is the unit ball of the Lipschitz-free Banach space associated wi…
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,…
On Rogers-Shephard type inequalities for general measures
David Alonso-Gutiérrez, María A. Hernández Cifre, Michael Roysdon +2
In this paper we prove a series of Rogers-Shephard type inequalities for convex bodies when dealing with measures on the Euclidean space with either radially decreasing densities,…