On the Carathéodory number for strong convexity

Abstract

We give an improvement of the Carathéodory theorem for strong convexity (ball convexity) in ${\mathbb{R}}^n$, reducing the Carathéodory number to $n$ in several cases; and show that the Carathéodory number cannot be smaller than $n$ for an arbitrary gauge body $K$. We also give an improved topological criterion for one convex body to be a Minkowski summand of another.

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References in corpus (2)

• Ball Convex Bodies in Minkowski Spaces
• Colorful theorems for strong convexity