# Optimal isometries for a pair of compact convex subsets of ℝⁿ

Irmina Herburt; Maria Moszyńska

Banach Center Publications (2009)

- Volume: 84, Issue: 1, page 111-120
- ISSN: 0137-6934

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topIrmina Herburt, and Maria Moszyńska. "Optimal isometries for a pair of compact convex subsets of ℝⁿ." Banach Center Publications 84.1 (2009): 111-120. <http://eudml.org/doc/281974>.

@article{IrminaHerburt2009,

abstract = {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.},

author = {Irmina Herburt, Maria Moszyńska},

journal = {Banach Center Publications},

keywords = {convex bodies; Hausdorff metric; metric; symmetric difference metric; optimal isometry; selector},

language = {eng},

number = {1},

pages = {111-120},

title = {Optimal isometries for a pair of compact convex subsets of ℝⁿ},

url = {http://eudml.org/doc/281974},

volume = {84},

year = {2009},

}

TY - JOUR

AU - Irmina Herburt

AU - Maria Moszyńska

TI - Optimal isometries for a pair of compact convex subsets of ℝⁿ

JO - Banach Center Publications

PY - 2009

VL - 84

IS - 1

SP - 111

EP - 120

AB - 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.

LA - eng

KW - convex bodies; Hausdorff metric; metric; symmetric difference metric; optimal isometry; selector

UR - http://eudml.org/doc/281974

ER -