Geodesic
The Fermat--Steiner problem in the space of compact subsets of the Euclidean plane
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 44-55

Voir la notice de l'article provenant de la source Math-Net.Ru

The Fermat–Steiner problem if the problem of finding all points of a metric space $Y$ such that the sum of the distances from them to points of a certain fixed finite subset $A$ of the space $Y$ is minimal. In this paper, we examine the Fermat–Steiner problem in the case where $Y$ is the space of compact subsets of the Euclidean plane endowed with the Hausdorff metric, and points of $A$ are finite pairwise disjoint compact sets.
Keywords: Fermat–Steiner problem, compact subset, Euclidean space, Steiner compact.
Mots-clés : Hausdorff distance 
@article{INTO_2020_175_a4,
     author = {A. H. Galstyan},
     title = {The {Fermat--Steiner} problem in the space of compact subsets of the {Euclidean} plane},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {44--55},
     publisher = {mathdoc},
     volume = {175},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_175_a4/}
}
TY  - JOUR
AU  - A. H. Galstyan
TI  - The Fermat--Steiner problem in the space of compact subsets of the Euclidean plane
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 44
EP  - 55
VL  - 175
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_175_a4/
LA  - ru
ID  - INTO_2020_175_a4
ER  - 
%0 Journal Article
%A A. H. Galstyan
%T The Fermat--Steiner problem in the space of compact subsets of the Euclidean plane
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 44-55
%V 175
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_175_a4/
%G ru
%F INTO_2020_175_a4
A. H. Galstyan. The Fermat--Steiner problem in the space of compact subsets of the Euclidean plane. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018», November 23-28, 2018, Kazan. Part 1, Tome 175 (2020), pp. 44-55. http://geodesic.mathdoc.fr/item/INTO_2020_175_a4/