3 papers
math.FA2021
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…
math.MG2020
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…
math.MG2019
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…