14 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…
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…
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…