14 citations · 35 across the 21 of their papers we have counts for
23 papers
The maximum volume polytope with nine vertices inscribed in the sphere
Steven Hoehner, Jeff Ledford
A classical problem in convex and discrete geometry asks for the convex polyhedron of greatest volume whose vertices are chosen from the unit sphere . For a prescribe…
Dual volume approximation of the Euclidean ball by polytopes with a fixed number of -faces
Steven Hoehner, Carsten Schütt, Elisabeth M. Werner
We study dual volume approximation of the Euclidean ball by polytopes with a prescribed number of -dimensional faces. This continues the authors' previous work on intrinsic volu…
Blaschke operations on log-concave functions and affine isoperimetric inequalities
Effrosyni Chasioti, Steven Hoehner
We introduce Blaschke addition and homothety operations on log-concave functions and study their affine-geometric consequences. Our starting point is the first variation formula of…
Generalized outer linearizations and extremal properties of rotational epi-symmetrizations
Steven Hoehner, Fabian Mussnig
We develop a functional extension of an extremal principle by Schneider (Monatsh. Math., 1967) by introducing generalized outer linearizations of convex functions. Given a coercive…
Central Limit Theorem for Random Partial Sphere Coverings in High Dimensions
Steven Hoehner, Christoph Thäle
We study a random partial covering model on the -dimensional unit sphere, where spherical caps are placed independently and uniformly at random, each covering a surface…
Simultaneous random polytope approximation characterizes the Euclidean ball
Steven Hoehner
In this work, we present a new geometric characterization of the Euclidean ball based on approximation by random polytopes. We investigate when a single boundary sampling density i…
From Circles to Convex Bodies: Approximating Curved Shapes by Polytopes
Steven Hoehner
Polytopes are the basic finite data structures for convex sets: they appear as feasible regions in linear optimization, as geometric summaries in algorithms, and as random objects…
Approximation of the Euclidean ball by polytopes with a fixed number of -faces
Steven Hoehner, Carsten Schütt, Elisabeth Werner
We derive lower estimates for the approximation of the -dimensional Euclidean ball by polytopes with a fixed number of -dimensional faces, . The metri…
New fiber and graph combinations of convex bodies
Steven Hoehner, Sudan Xing
Three new combinations of convex bodies are introduced and studied: the fiber, chord and graph combinations. These combinations are defined in terms of the fibers and g…
On the Optimality of Random Partial Sphere Coverings in High Dimensions
Steven Hoehner, Gil Kur
Given geodesic caps on the unit sphere in , whose total normalized surface area is one, what is the maximal proportion of the sphere that their union can cover? I…
Steiner symmetrization on the sphere
Bushra Basit, Steven Hoehner, Zsolt Lángi +1
The aim of this paper is to introduce a generalization of Steiner symmetrization in Euclidean space for spherical space, which is the dual of the Steiner symmetrization in hyperbol…
On maximal intersection position for logarithmically concave functions and measures
Steven Hoehner, Michael Roysdon
A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex…
An extremal property of the symmetric decreasing rearrangement
Steven Hoehner, Júlia Novaes
It is shown that for a given log-concave function, its symmetric decreasing rearrangement is always harder to approximate in the symmetric difference metric by inner log-linearizat…
On Minkowski symmetrizations of -concave functions and related applications
Steven Hoehner
The Minkowski symmetral of an -concave function is studied, and some of its fundamental properties are derived. It is shown that for a given -concave function, there exists a…
Surface areas of equifacetal polytopes inscribed in the unit sphere
Nicolas Freeman, Steven Hoehner, Jeff Ledford +2
This article is concerned with the problem of placing seven or eight points on the unit sphere in so that the surface area of the convex hull of the p…
An intrinsic volume metric for the class of convex bodies in
Florian Besau, Steven Hoehner
A new intrinsic volume metric is introduced for the class of convex bodies in . As an application, an inequality is proved for the asymptotic best approximation of th…
Extremal arrangements of points on the sphere for weighted cone-volume functionals
Steven Hoehner, Jeff Ledford
Weighted cone-volume functionals are introduced for the convex polytopes in . For these functionals, geometric inequalities are proved and the equality conditions are…
Asymptotic expected -functionals of random polytopes with applications to surface areas
Steven Hoehner, Ben Li, Michael Roysdon +1
An asymptotic formula is proved for the expected -functional of the convex hull of independent and identically distributed random points sampled from the Euclidean unit sphere i…
Extremal general affine surface areas
Steven Hoehner
For a convex body in , we introduce and study the extremal general affine surface areas, defined by \[ {\rm IS}_φ(K):=\sup_{K^\prime\subset K}{\rm as}_φ(K),\quad…
The Maximum Surface Area Polyhedron with Five Vertices Inscribed in the Sphere
Jessica Donahue, Steven Hoehner, Ben Li
This article focuses on the problem of analytically determining the optimal placement of five points on the unit sphere so that the surface area of the convex hull o…
Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes
Florian Besau, Steven Hoehner, Gil Kur
We establish estimates for the asymptotic best approximation of the Euclidean unit ball by polytopes under a notion of distance induced by the intrinsic volumes. We also introduce…
A Concentration Inequality for Random Polytopes, Dirichlet-Voronoi Tiling Numbers and the Geometric Balls and Bins Problem
Steven Hoehner, Gil Kur
Our main contribution is a concentration inequality for the symmetric volume difference of a convex body with positive Gaussian curvature and a circumscribed random polytop…
The Surface Area Deviation of the Euclidean Ball and a Polytope
Steven D. Hoehner, Carsten Schuett, Elisabeth M. Werner
While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Her…