Geodesic
Steiner points in $l_\infty^2$ spaсe
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2023), pp. 14-19 
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/
@article{VMUMM_2023_1_a1,
     author = {B. B. Bednov},
     title = {Steiner points in $l_\infty^2$ spa{\cyrs}e},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {14--19},
     year = {2023},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a1/}
}
TY  - JOUR
AU  - B. B. Bednov
TI  - Steiner points in $l_\infty^2$ spaсe
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2023
SP  - 14
EP  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a1/
LA  - ru
ID  - VMUMM_2023_1_a1
ER  - 
%0 Journal Article
%A B. B. Bednov
%T Steiner points in $l_\infty^2$ spaсe
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2023
%P 14-19
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2023_1_a1/
%G ru
%F VMUMM_2023_1_a1

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

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.

[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