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Minimal pairs of convex bodies in two dimensions

Scholtes, S (1992) Minimal pairs of convex bodies in two dimensions. Mathematika, 39. pp. 267-273. ISSN 0025-5793

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In [7] the notion of minimal pairs of convex compact subsets of a Hausdorff topological vector space was introduced and it was conjectured, that minimal pairs in an equivalence class of the Hörmander-Rådström lattice are unique up to translation. We prove this statement for the two-dimensional case. To achieve this we prove a necessary and sufficient condition in terms of mixed volumes that a translate of a convex body in ℝn is contained in another convex body. This generalizes a theorem of Weil (cf. [10]).

Item Type: Article
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 20:34
Last Modified: 12 Jun 2018 01:58