The Fermat–Steiner Problem in the Space of Compact Subsets of the Euclidean Plane

The Fermat–Steiner problem is 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 su...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 272; no. 6; pp. 791 - 802
Main Author Galstyan, A. H.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 02.06.2023
Springer
Springer Nature B.V
Subjects
Euclidean geometry
Mathematics
Mathematics and Statistics
Metric space
compact subset
Hausdorff distance
Euclidean space
51E99
Steiner compact
Fermat–Steiner problem
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-023-06473-3

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Summary:The Fermat–Steiner problem is 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.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06473-3