Determining starshaped sets and unions of starshaped sets by their sections (Q1821353)

The aim of the paper is to characterize a compact set in \({\mathbb{R}}^ d\) to be a starshaped set or a union of starshaped sets by corresponding properties of k-dimensional sections of the set. As a typical result we mention a corollary of the main theorem (which is too involved to be described here): Let S be a compact set in \({\mathbb{R}}^ d\) and fix a point \(p\in S\) and an integer k, \(1\leq k<d\). Then S is starshaped in view of p iff \(F\cap S\) is starshaped for every k-flat F through p.