Stability of Blaschke's characterization of ellipsoids and Radon norms (Q1356079)

The author presents stability versions of classical characterization results in convex geometry. The first result extends a theorem of Blaschke, it shows that a convex body in \(\mathbb{R}^d\), \(d\geq 3\), which has almost planar shadow boundaries is almost an ellipsoid. The second result proves that a planar convex body which has almost conjugate diameters is close (in the Banach-Mazur distance) to a Radon disk. Some consequences are also given.