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

Agnieszka Bogdewicz; Jerzy Grzybowski

Banach Center Publications, Tome 86 (2009), p. 75-88 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $(ℝ, | | \cdot | |_{)}$ be a Minkowski space with a unit ball and let $ϱ_{H}^{}$ be the Hausdorff metric induced by ${| | \cdot | |}_{}$ 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 $ϱ_{H}^{B ⁿ}$ for the Euclidean unit ball Bⁿ. We extend Schneider’s theorem to the hyperspace $(², ϱ_{H}^{})$ over any two-dimensional Minkowski space.

Publié le : 2009-01-01

Zbl 1181.52004

EUDML-ID : urn:eudml:doc:281750

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     author = {Agnieszka Bogdewicz and Jerzy Grzybowski},
     title = {Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment},
     journal = {Banach Center Publications},
     volume = {86},
     year = {2009},
     pages = {75-88},
     zbl = {1181.52004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc84-0-5}
}

Agnieszka Bogdewicz; Jerzy Grzybowski. Pairs of convex bodies in a hyperspace over a Minkowski two-dimensional space joined by a unique metric segment. Banach Center Publications, Tome 86 (2009) pp. 75-88. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc84-0-5/