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

• Autorzy: Agnieszka Bogdewicz , Jerzy Grzybowski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 52A21: Finite-dimensional Banach spaces (including special norms, zonoids, etc.)
• 52A10: Convex sets in 2 dimensions (including convex curves)
• 52A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 84
• Numer: 1
• Strony: 75-88

Daty

wydano

2009

Twórcy

autor

Agnieszka Bogdewicz

• Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warszawa, Poland

autor

Jerzy Grzybowski

• Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

Identyfikatory

DOI

10.4064/bc84-0-5