Journal of Convex Analysis 29 (2022), No. 3, 807--826
Copyright Heldermann Verlag 2022
Boundedly Polyhedral Sets and F-Simplices
Valeriu Soltan
Dept. of Mathematical Sciences, George Mason University, Fairfax, U.S.A.
vsoltan@gmu.edu
[Abstract-pdf]
Generalizing the concept of Choquet simplex, we study a new class of convex solids $K$ in $\mathbb{R}^n$ which satisfy the following condition: all $n$-dimensional intersections of the form $K \cap (x + K)$, $x \in \mathbb{R}^n$, belong to at most finitely many homothety classes of convex solids. Our description of this class uses new results on boundedly polyhedral sets.
Keywords: Convex set, Choquet simplex, homothety class, polyhedron.
MSC: 52A20.
[ Fulltext-pdf (156 KB)] for subscribers only.