Colorful theorems for strong convexity
Combinatorics
2017-03-21 v2 Metric Geometry
Abstract
We prove two colorful Carath\'eodory theorems for strongly convex hulls, generalizing the colorful Carat\'eodory theorem for ordinary convexity by Imre B\'ar\'any, the non-colorful Carath\'eodory 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.
Cite
@article{arxiv.1509.08783,
title = {Colorful theorems for strong convexity},
author = {Andreas F. Holmsen and Roman Karasev},
journal= {arXiv preprint arXiv:1509.08783},
year = {2017}
}