Abstract
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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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 175, Proceedings of the XVII All-Russian Youth School-Conference “Lobachevsky Readings-2018,” November 23-28, 2018, Kazan. Part 1, 2020.
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Galstyan, A.H. The Fermat–Steiner Problem in the Space of Compact Subsets of the Euclidean Plane. J Math Sci 272, 791–802 (2023). https://doi.org/10.1007/s10958-023-06473-3
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DOI: https://doi.org/10.1007/s10958-023-06473-3