The Christoffel problem for the disk area measure
Leo Brauner, Georg C. Hofstätter, Oscar Ortega-Moreno
公開日: 2025/8/13
Abstract
The mixed Christoffel problem asks for necessary and sufficient conditions for a Borel measure on the Euclidean unit sphere to be the mixed area measure of some convex bodies, all but one of them are fixed. We provide a solution in the case where the fixed reference bodies are (n-1)-dimensional disks with parallel axes and the measure has no mass at the poles of the sphere determined by this axis.