# Fractal star bodies

Irmina Herburt; Maria Moszyńska; Dorette Pronk

Banach Center Publications (2009)

- Volume: 84, Issue: 1, page 149-171
- ISSN: 0137-6934

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topIrmina Herburt, Maria Moszyńska, and Dorette Pronk. "Fractal star bodies." Banach Center Publications 84.1 (2009): 149-171. <http://eudml.org/doc/281762>.

@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, Dorette Pronk},

journal = {Banach Center Publications},

keywords = {fractals; star bodies},

language = {eng},

number = {1},

pages = {149-171},

title = {Fractal star bodies},

url = {http://eudml.org/doc/281762},

volume = {84},

year = {2009},

}

TY - JOUR

AU - Irmina Herburt

AU - Maria Moszyńska

AU - Dorette Pronk

TI - Fractal star bodies

JO - Banach Center Publications

PY - 2009

VL - 84

IS - 1

SP - 149

EP - 171

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 - fractals; star bodies

UR - http://eudml.org/doc/281762

ER -

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