F. Fodor

activity

20092026

most citedThe

L_{p}

dual Minkowski problem for

p > 1

and

q > 0

73 citations · 171 across the 26 of their papers we have counts for

collaborators

26 papers

math.MG2026

Sylvester's four point problem for ball-convex bodies

Alexandra Bakó-Szabó, Florian Besau, Ferenc Fodor

We investigate Sylvester's classical four-point problem for ball-convex bodies, where convex hulls are replaced by intersections of balls of a fixed radius $R$ . We show that the Ef…

math.MG2025

Central diagonal sections of Gaussian cubes

Ferenc Fodor, Bernardo González Merino

The investigation of the volume, surface area, and other geometric properties of sections of convex bodies, and in particular cubes, has a long history and a rich literature. Howev…

math.MG2025

On generalized disc-polygons in plane convex bodies with a higher degree of smoothness

Ferenc Fodor, Dániel I. Papvári

We prove power series expansions for the expectations of the number of vertices and missed area of random $L$ -convex polygons in planar convex bodies with sufficiently smooth bound…

math.MG2025

Variances and central limit theorems for random beta-polytopes and in other geometric models

Ferenc Fodor, Balázs Grünfelder

We prove matching asymptotic lower and upper bounds on the variances of the intrinsic volumes and the number of $k$ -faces of $d$ -dimensional random beta-polytopes. Using Stein's me…

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

On the minimal area of quadrangles circumscribed about planar convex bodies

Ferenc Fodor, Florian Grundbacher

We show that every planar convex body is contained in a quadrangle whose area is less than $(1 - 2.6 \cdot 1 0^{- 7}) 2$ times the area of the original convex body, improving…

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

A central limit theorem for random disc-polygons in smooth convex discs

Ferenc Fodor, Dániel I. Papvári

In this paper we prove a quantitative central limit theorem for the area of uniform random disc-polygons in smooth convex discs whose boundary is $C_{+}^{2}$ . We use Stein's method and…

math.MG2021★ 3 cited

Variance bounds for disc-polygons

Ferenc Fodor, Balázs Grünfelder, Viktor Vígh

We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is $C_{+}^{2}$ smooth. The established…

math.MG2021★ 2 cited

On random disc-polygons in a disc-polygon

Ferenc Fodor, Péter Kevei, Viktor Vígh

We prove asymptotic formulas for the expectation of the vertex number and missed area of uniform random disc-polygons in convex disc-polygons. Our statements are the $r$ -convex ana…

math.MG2020★ 5 cited

Central diagonal sections of the $n$ -cube

Ferenc Bartha, Ferenc Fodor, Bernardo González Merino

We prove that the volume of central hyperplane sections of a unit cube in $R^{n}$ orthogonal to a diameter of the cube is a strictly monotonically increasing function of the…

math.MG2020★ 5 cited

Strengthened inequalities for the mean width and the $ℓ$ -norm

Károly J. Böröczky, Ferenc Fodor, Daniel Hug

Barthe proved that the regular simplex maximizes the mean width of convex bodies whose John ellipsoid (maximal volume ellipsoid contained in the body) is the Euclidean unit ball; o…

math.MG2019

On random approximations by generalized disc-polygons

Ferenc Fodor, Dániel I. Papvári, Viktor Vígh

For two convex discs $K$ and $L$ , we say that $K$ is $L$ -convex if it is equal to the intersection of all translates of $L$ that contain $K$ . In $L$ -convexity the set $L$ plays a s…

math.MG2019★ 1 cited

Random ball-polytopes in smooth convex bodies

Ferenc Fodor

We study approximations of smooth convex bodies by random ball-polytopes. We examine the following probability model: let $K \subset R^{d}$ be a convex body such that $K$ slides…

math.MG2019

Perimeter approximation of convex discs in the hyperbolic plane and on the sphere

Ferenc Fodor

Eggleston (1957) proved that in the Euclidean plane the best approximating convex $n$ -gon to a convex disc $K$ is always inscribed in $K$ if we measure the distance by perimeter de…

math.MG2018★ 2 cited

On the volume bound in the Dvoretzky--Rogers lemma

Ferenc Fodor, Márton Naszódi, Tamás Zarnócz

The classical Dvoretzky--Rogers lemma provides a deterministic algorithm by which, from any set of isotropic vectors in Euclidean $d$ -space, one can select a subset of $d$ vectors…

math.MG2018★ 9 cited

Variance estimates for random disc-polygons in smooth convex discs

Ferenc Fodor, Viktor Vígh

In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed area of inscribed random disc-polygons in smooth convex discs whose boundary is…

math.AP2018★ 73 cited

The $L_{p}$ dual Minkowski problem for $p > 1$ and $q > 0$

Károly J. Böröczky, Ferenc Fodor

General $L_{p}$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang. These new measures unify several other geometric measures of the Brunn-Minkowski theo…

math.MG2017★ 1 cited

On the multiplicity of arrangements of congruent zones on the sphere

A. Bezdek, F. Fodor, V. Vígh +1

Consider an arrangement of $n$ congruent zones on the $d$ -dimensional unit sphere $S^{d - 1}$ , where a zone is the intersection of an origin symmetric Euclidean plank with $S^{d - 1}$ .…

math.PR2016★ 1 cited

Strengthened volume inequalities for L_p zonoids of even isotropic measures

Karoly J. Boroczky, Ferenc Fodor, Daniel Hug

We strengthen the volume inequalities for L_p zonoids of even isotropic measures and for their duals, which are due to Ball, Barthe and Lutwak, Yang, Zhang. Along the way, we prove…

math.MG2015★ 8 cited

The packing density of the $n$ -dimensional cross-polytope

G. Fejes Tóth, F. Fodor, V. Vígh

The packing density of the regular cross-polytope in Euclidean $n$ -space is unknown except in dimensions $2$ and $4$ where it is 1. The only non-trivial upper bound is due to Grave…

math.MG2014★ 6 cited

A fractional Helly theorem for boxes

I. Bárány, F. Fodor, A. Martínez-Pérez +3

Let $F$ be a family of $n$ axis-parallel boxes in $R^{d}$ and $α \in (1 - 1/ d, 1]$ a real number. There exists a real number $β (α) > 0$ such that if there are $α{n\choos…

math.MG2014★ 8 cited

The volume of random polytopes circumscribed around a convex body

Ferenc Fodor, Daniel Hug, Ines Ziebarth

Let $K$ be a convex body in $R^{d}$ which slides freely in a ball. Let $K^{(n)}$ denote the intersection of $n$ closed half-spaces containing $K$ whose bounding hyperplanes…

math.MG2011★ 13 cited

Intrinsic volumes of random polytopes with vertices on the boundary of a convex body

Károly J. Böröczky, Ferenc Fodor, Daniel Hug

Let $K$ be a convex body in $R^{d}$ , let $j \in {1, ..., d - 1}$ , and let $ϱ$ be a positive and continuous probability density function with respect to the $(d - 1)$ -dimensional H…

Sylvester's four point problem for ball-convex bodies

Central diagonal sections of Gaussian cubes

On generalized disc-polygons in plane convex bodies with a higher degree of smoothness

Variances and central limit theorems for random beta-polytopes and in other geometric models

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

On the minimal area of quadrangles circumscribed about planar convex bodies

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

A central limit theorem for random disc-polygons in smooth convex discs

Variance bounds for disc-polygons

On random disc-polygons in a disc-polygon

Central diagonal sections of the n-cube

Strengthened inequalities for the mean width and the ℓ-norm

On random approximations by generalized disc-polygons

Random ball-polytopes in smooth convex bodies

Perimeter approximation of convex discs in the hyperbolic plane and on the sphere

On the volume bound in the Dvoretzky--Rogers lemma

Variance estimates for random disc-polygons in smooth convex discs

The Lp​ dual Minkowski problem for p>1 and q>0

On the multiplicity of arrangements of congruent zones on the sphere

Strengthened volume inequalities for L_p zonoids of even isotropic measures

The packing density of the n-dimensional cross-polytope

A fractional Helly theorem for boxes

The volume of random polytopes circumscribed around a convex body

Intrinsic volumes of random polytopes with vertices on the boundary of a convex body

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

Central diagonal sections of the $n$ -cube

Strengthened inequalities for the mean width and the $ℓ$ -norm

The $L_{p}$ dual Minkowski problem for $p > 1$ and $q > 0$

The packing density of the $n$ -dimensional cross-polytope