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

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Bogdewicz A., Grzybowski J.

Banach Center Publications

2009

tom 84

nr 1

75-88

Let $(ℝ,||·||_𝔹)$ be a Minkowski space with a unit ball 𝔹 and let $ϱ_H^{𝔹}$ be the Hausdorff metric induced by $||·||_{𝔹}$ in the hyperspace 𝒦 of convex bodies (nonempty, compact, convex subsets of ℝ). R. Schneider [RSP] characterized pairs of elements of 𝒦 which can be joined by unique metric segments with respect to $ϱ_H^{Bⁿ}$ for the Euclidean unit ball Bⁿ. We extend Schneider's theorem to the hyperspace $(𝒦²,ϱ_H^{𝔹})$ over any two-dimensional Minkowski space.

Ograniczanie wyników

1 Banach Center Publications

1 Bogdewicz A.

1 Grzybowski J.

1 2009

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