Affine diameters of convex bodies -- a survey
Given a convex body \(K\) in \(\mathbb{R}^{d}\), and two points \(a,b\) in the boundary of \(K\), the closed segment with endpoints \(a, b\) is an affine diameter of \(K\) if there exist two distinct parallel hyperplanes supporting \(K\) at \(a\) and \(b\), respectively. Examples of affine diameters are provided by the usual diameter, and double normals of \(K\). In this survey the author reviews basic properties of affine diameters and discusses known results and open problems regarding various topics related to this notion, e.g. characterizations of centrally symmetric convex bodies, measures of symmetry, orthogonality in linear normed spaces.
scientific article; zbMATH DE number 2175361
scientific article