Colorful theorems for strong convexity
arXiv:1509.08783 · doi:10.1090/proc/13405
Abstract
We prove two colorful Carathéodory theorems for strongly convex hulls, generalizing the colorful Caratéodory theorem for ordinary convexity by Imre Bárány, the non-colorful Carathéodory theorem for strongly convex hulls by the second author, and the "very colorful theorems" by the first author and others. We also investigate if the assumption of a "generating convex set" is really needed in such results and try to give a topological criterion for one convex body to be a Minkowski summand of another.