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arXiv · 1509.08783

Colorful theorems for strong convexity

Andreas F. Holmsen·Roman Karasev
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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.

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Andreas F. Holmsen, Roman Karasev. 2016-08-01. Colorful theorems for strong convexity. https://doi.org/10.1090/proc%2F13405

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