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Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment

Agnieszka Bogdewicz, Jerzy Grzybowski (2009)

Banach Center Publications

Let ( , | | · | | ) be a Minkowski space with a unit ball and let ϱ H be the Hausdorff metric induced by | | · | | in the hyperspace of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of which can be joined by unique metric segments with respect to ϱ H B for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace ( ² , ϱ H ) over any two-dimensional Minkowski space.

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