HUN-REN Alfréd Rényi Institute of Mathematics

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19942026

most citedBrownian distance covariance

857 citations

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Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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68 papers · 1 filter

math.MG2025

Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality

Karoly J. Böröczky, Ferenc Fodor, Pavlos Kalantzopoulos

We use the characterization of the case of equality in Barthe's Geometric Reverse Brascamp-Lieb inequality to characterize equality in Liakopoulos's volume estimate in terms of sec…

math.MG2025

A note on the Steinitz Lemma

Gergely Ambrus, Rainie Heck

We establish the connection between the Steinitz problem for ordering vector families in arbitrary norms and its variant for not necessarily zero-sum families consisting of `nearly…

math.MG2025

Covering spiky annuli by planks

Gergely Ambrus, Julian Huddell, Maggie Lai +2

Answering Tarski's plank problem, Bang showed in 1951 that it is impossible to cover a convex body $K \subset R^{d}$ with $d \geq 1$ by planks whose total width is less than…

math.MG2025★ 391 cited

The Logarithmic Minkowski Problem

Károly J. Böröczky, Erwin Lutwak, Deane Yang +1

In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the u…

math.MG2024

Estimates on the decay of the Laplace-Polya integral

Gergely Ambrus, Barnabás Gárgyán

The Laplace--Pólya integral, defined by $J_{n} (r) = \frac{1}{π} \int_{- \infty}^{\infty} sinc^{n} t cos (r t) d t$ , appears in several areas of mathematics. We study this q…

math.MG2024★ 1 cited

Isometric rigidity of the Wasserstein space over the plane with the maximum metric

Zoltán M. Balogh, Gergely Kiss, Tamás Titkos +1

We study $p$ -Wasserstein spaces over the branching spaces $R^{2}$ and $[- 1, 1]^{2}$ equipped with the maximum norm metric. We show that these spaces are isometrically rigid for…

math.MG2024★ 1 cited

Strengthened inequalities for the mean width and the $ℓ$ -norm of origin symmetric convex bodies

Károly J. Böröczky, Ferenc Fodor, Daniel Hug

Barthe, Schechtman and Schmuckenschläger proved that the cube maximizes the mean width of symmetric convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the bo…

math.MG2023

On Axial Symmetry in Convex Bodies

Ritesh Goenka, Kenneth Moore, Wen Rui Sun +1

For a two-dimensional convex body, the Kovner-Besicovitch measure of symmetry is defined as the volume ratio of the largest centrally symmetric body contained inside the body to th…

math.MG2023★ 2 cited

Isometric rigidity of Wasserstein spaces over Euclidean spheres

György Pál Gehér, Aranka Hrušková, Tamás Titkos +1

We study the structure of isometries of the quadratic Wasserstein space $W_{2} (S^{n}, ∥ \cdot ∥)$ over the sphere endowed with the distance inherited from…

math.MG2023★ 4 cited

A note on Borsuk's problem in Minkowski spaces

Andrei M. Raigorodskii, Arsenii Sagdeev

In 1993, Kahn and Kalai famously constructed a sequence of finite sets in $d$ -dimensional Euclidean spaces that cannot be partitioned into less than $(1.203 \dots + o (1))^{d}$ …

math.MG2023★ 1 cited

Non-diagonal critical central sections of the cube

Gergely Ambrus, Barnabás Gárgyán

We study the $(n - 1)$ -dimensional volume of central hyperplane sections of the $n$ -dimensional cube $Q_{n}$ . Our main goal is two-fold: first, we provide an alternative, simpler argum…

math.MG2023

On optimal $λ$ -separable packings in the plane

Károly Bezdek, Zsolt Lángi

Let $P$ be a packing of circular disks of radius $ρ > 0$ in the Euclidean, spherical, or hyperbolic plane. Let $0 \leq λ \leq ρ$ . We say that $P$ is a $λ$ -separable p…

math.MG2023

Isometric rigidity of the Wasserstein space $W_{1} (G)$ over Carnot groups

Zoltán M. Balogh, Tamás Titkos, Dániel Virosztek

This paper aims to study isometries of the $1$ -Wasserstein space $W_{1} (G)$ over Carnot groups endowed with horizontally strictly convex norms. Well-known examples…

math.MG2023★ 4 cited

Isometries and isometric embeddings of Wasserstein spaces over the Heisenberg group

Zoltán M. Balogh, Tamás Titkos, Dániel Virosztek

Our purpose in this paper is to study isometries and isometric embeddings of the $p$ -Wasserstein space $W_{p} (H^{n})$ over the Heisenberg group $H^{n}$ for al…

math.MG2023★ 3 cited

Colorful Vector Balancing

Gergely Ambrus, Rainie Bozzai

We extend classical estimates for the vector balancing constant of $R^{d}$ equipped with the Euclidean and the maximum norms proved in the 1980's by showing that for $p = 2$ …

math.MG2022★ 3 cited

Functional John and Löwner conditions for pairs of log-concave functions

Grigory Ivanov, Márton Naszódi

John's fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ in $R^{d}$ has seen several generalizations and extensions. One directi…

math.MG2022★ 6 cited

Quantitative Steinitz Theorem: A polynomial bound

Grigory Ivanov, Márton Naszódi

The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set $S \subset R^{d}$ , then there are at most $2 d$ points of $S$ who…

math.MG2022★ 4 cited

The density of planar sets avoiding unit distances

Gergely Ambrus, Adrián Csiszárik, Máté Matolcsi +2

By improving upon previous estimates on a problem posed by L. Moser, we prove a conjecture of Erdős that the density of any measurable planar set avoiding unit distances cannot exc…

math.MG2022★ 10 cited

Isometric rigidity of Wasserstein tori and spheres

György Pál Gehér, Tamás Titkos, Dániel Virosztek

We prove isometric rigidity for $p$ -Wasserstein spaces over finite-dimensional tori and spheres for all $p$ . We present a unified approach to proving rigidity that relies on the ro…

math.MG2022★ 4 cited

Two-colorings of normed spaces without long monochromatic unit arithmetic progressions

Valeriya Kirova, Arsenii Sagdeev

Given a natural $n$ , we construct a two-coloring of $R^{n}$ with the maximum metric satisfying the following. For any finite set of reals $S$ with diameter greater than $5^{…

math.MG2022★ 7 cited

Odd-distance and right-equidistant sets in the maximum and Manhattan metrics

Alexander Golovanov, Andrey Kupavskii, Arsenii Sagdeev

We solve two related extremal-geometric questions in the $n -$ dimensional space $R_{\infty}^{n}$ equipped with the maximum metric. First, we prove that the maximum size of a…

math.MG2021★ 2 cited

Nonstandard $n$ -distances based on certain geometric constructions

Gergely Kiss, Jean-Luc Marichal

The concept of $n$ -distance was recently introduced to generalize the classical definition of distance to functions of $n$ arguments. In this paper we investigate this concept thro…

math.MG2021★ 13 cited

The isometry group of Wasserstein spaces: the Hilbertian case

György Pál Gehér, Tamás Titkos, Dániel Virosztek

Motivated by Kloeckner's result on the isometry group of the quadratic Wasserstein space $W_{2} (R^{n})$ , we describe the isometry group $\mathrm{Isom}\lef…

math.MG2020★ 2 cited

Large signed subset sums

Gergely Ambrus, Bernardo González Merino

We study the following question: for given $d \geq 2$ , $n \geq d$ and $k \leq n$ , what is the largest value $c (d, n, k)$ such that from any set of $n$ unit vectors in $R^{d}$ , w…

Equality in Liakopoulos's generalized dual Loomis-Whitney inequality via Barthe's Reverse Brascamp-Lieb inequality

A note on the Steinitz Lemma

Covering spiky annuli by planks

The Logarithmic Minkowski Problem

Estimates on the decay of the Laplace-Polya integral

Isometric rigidity of the Wasserstein space over the plane with the maximum metric

Strengthened inequalities for the mean width and the ℓ-norm of origin symmetric convex bodies

On Axial Symmetry in Convex Bodies

Isometric rigidity of Wasserstein spaces over Euclidean spheres

A note on Borsuk's problem in Minkowski spaces

Non-diagonal critical central sections of the cube

On optimal λ-separable packings in the plane

Isometric rigidity of the Wasserstein space W1​(G) over Carnot groups

Isometries and isometric embeddings of Wasserstein spaces over the Heisenberg group

Colorful Vector Balancing

Functional John and Löwner conditions for pairs of log-concave functions

Quantitative Steinitz Theorem: A polynomial bound

The density of planar sets avoiding unit distances

Isometric rigidity of Wasserstein tori and spheres

Two-colorings of normed spaces without long monochromatic unit arithmetic progressions

Odd-distance and right-equidistant sets in the maximum and Manhattan metrics

Nonstandard n-distances based on certain geometric constructions

The isometry group of Wasserstein spaces: the Hilbertian case

Large signed subset sums

Strengthened inequalities for the mean width and the $ℓ$ -norm of origin symmetric convex bodies

On optimal $λ$ -separable packings in the plane

Isometric rigidity of the Wasserstein space $W_{1} (G)$ over Carnot groups

Nonstandard $n$ -distances based on certain geometric constructions