COLORFUL THEOREMS FOR STRONG CONVEXITY

We prove two colorful Caratheodory theorems for strongly convex hulls, generalizing the colorful Caratheodory theorem for ordinary convexity by Imre Barany, the non-colorful Caratheodory 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.
Publisher
AMER MATHEMATICAL SOC
Issue Date
2017-06
Language
English
Keywords

HELLY THEOREM; NUMBERS; HOMOLOGY

Citation

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, v.145, no.6, pp.2713 - 2726

ISSN
0002-9939
DOI
10.1090/proc/13405
URI
http://hdl.handle.net/10203/223643
Appears in Collection
MA-Journal Papers(저널논문)
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