Optimal isometries for a pair of compact convex subsets of ℝⁿ

Irmina 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 -