Geodesic
Steiner points in $l_\infty^2$ spaсe
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 14-19

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It is proved that for a given set of pairwise distinct points $x_1, \dots, x_n$ the sum of the distances from these points to their Steiner point in $l_\infty^2$ space is equal to the maximum of the sum of lengths of $[\frac{n}{2}] - 1$ separate segments and either a semi-perimeter of a triangle, or another segment with vertices in this set. The case of coincident points among $x_1, \dots, x_n$ is also studied. 
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     author = {B. B. Bednov},
     title = {Steiner points in $l_\infty^2$ spa{\cyrs}e},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {14--19},
     publisher = {mathdoc},
     number = {1},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a1/}
}
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B. B. Bednov. Steiner points in $l_\infty^2$ spaсe. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 14-19. http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a1/