Fractal star bodies

• Autorzy: Irmina Herburt , Maria Moszyńska , Dorette Pronk
• Języki publikacji: EN

Abstrakty

EN

In 1989 R. Arnold proved that for every pair (A,B) of compact convex subsets of ℝ there is an Euclidean isometry optimal with respect to L₂ metric and if f₀ is such an isometry, then the Steiner points of f₀(A) and B coincide. In the present paper we solve related problems for metrics topologically equivalent to the Hausdorff metric, in particular for $L_p$ metrics for all p ≥ 2 and the symmetric difference metric.

Kategorie tematyczne

• 28A80: Fractals
• 52A30: Variants of convex sets (star-shaped, ( m , n )-convex, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 84
• Numer: 1
• Strony: 149-171

Daty

wydano

2009

Twórcy

autor

Irmina Herburt

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

autor

Maria Moszyńska

• Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

autor

Dorette Pronk

• Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 3J5, Canada

Identyfikatory

DOI

10.4064/bc84-0-10