Geodesic
Steiner points in $l_\infty^2$ spaсe
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 14-19 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Lima Å., “Intersection properties of balls and subspaces in Banach spaces”, Trans. Amer. Math. Soc., 227 (1977), 1–62

[2] Grothendieck A., “Une caractérisation vectorielle-métrique des espaces $L^1$”, Can. J. Math, 7:4 (1955), 552–561

[3] Lindenstrauss J., “Extension of compact operators”, Mem. Amer. Math. Soc., 48, 1964, 1–112

[4] Bednov B.B., Borodin P.A., “Banakhovy prostranstva, realizuyuschie minimalnye zapolneniya”, Matem. sb., 205:4 (2014), 3–19

[5] Bednov B.B., “Dlina minimalnogo zapolneniya tipa zvezdy”, Matem. sb., 207:8 (2016), 31–46

[6] Wolfe D., “A minimal point of a finite metric set”, J. Combin. Theory, 2 (1967), 514–522

[7] Bednov B.B., “O tochkakh Shteinera v prostranstve nepreryvnykh funktsii”, Vestn. Mosk. un-ta. Matem. Mekhan., 2011, no. 6, 26–31