# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Optimal isometries for a pair of compact convex subsets of $\mathbb R^n$

### Tom 84 / 2009

Banach Center Publications 84 (2009), 111-120 MSC: 52A20, 52A99, 41A65, 41A99. DOI: 10.4064/bc84-0-7

#### Streszczenie

In 1989 R. Arnold proved that for every pair $(A,B)$ of compact convex subsets of $\mathbb R$ there is an Euclidean isometry optimal with respect to $L_2$ metric and if $f_0$ is such an isometry, then the Steiner points of $f_0(A)$ 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 $p \ge 2$ and the symmetric difference metric.

#### Autorzy

• Irmina HerburtDepartment of Mathematics and Information Science
Warsaw University of Technology
Pl. Politechniki 1
00-661 Warszawa, Poland
e-mail
• Maria MoszyńskaInstitute of Mathematics
University of Warsaw
Banacha 2
02-097 Warszawa, Poland
e-mail

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