Homothetic floating bodies
The convex floating body \(K_ \delta\) of a convex body \(K\) in \(E^ d\) is the intersection of all halfspaces whose hyperplanes cut off a set of volume \(\delta\) from \(K\). Authors prove that \(K\) is an ellipsoid if there is a sequence \(\{\delta_ k\}_{k \in N}\) converging to 0 such that each \(K_{\delta_ k}\) is homothetic to \(K\) with respect to the same center of homothety.
scientific article; zbMATH DE number 569272