Convex geometry is a vibrant area of mathematics that investigates the properties and structure of convex sets in Euclidean spaces. This field is intrinsically linked to a series of fundamental ...

Abstract: In this article, we present an efficient unified algorithm for the minimum Euclidean distance between two collections of compact convex sets, each of which can be a collection of convex ...

Let Γ(X) denote the proper, lower semicontinuous, convex functions on a Banach space X, equipped with the completely metrizable topology of uniform convergence of distance functions on bounded sets.

In this article we prove two characterizations of the Euclidean ball: (i) the only convex body in ℝ³ such that every normal plane bisects the volume (or surface area) is the Euclidean ball, (ii) the ...