Abstract
In this paper we introduce the notion of a minimal convex annulusK (C) of a convex bodyC, generalizing the concept of a minimal circular annulus. Then we prove the existence — as for the minimal circular annulus — of a Radon partition of the set of contact points of the boundaries ofK (C) andC. Subsequently, the uniqueness ofK (C) is shown. Finally, it is proven that, for typicalC, the boundary ofC has precisely two points in common with each component of the boundary ofK (C).
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Peri, C., Zucco, A. On the minimal convex annulus of a planar convex body. Monatshefte für Mathematik 114, 125–133 (1992). https://doi.org/10.1007/BF01535579
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DOI: https://doi.org/10.1007/BF01535579