Geodesic
Banach spaces that realize minimal fillings
Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 459-475

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

It is proved that a real Banach space realizes minimal fillings for all its finite subsets (a shortest network spanning a fixed finite subset always exists and has the minimum possible length) if and only if it is a predual of $L_1$. The spaces $L_1$ are characterized in terms of Steiner points (medians). Bibliography: 25 titles.
Keywords: Banach space, shortest network, minimal filling, Steiner point (median). 
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B. B. Bednov; P. A. Borodin. Banach spaces that realize minimal fillings. Sbornik. Mathematics, Tome 205 (2014) no. 4, pp. 459-475. http://geodesic.mathdoc.fr/item/SM_2014_205_4_a0/