Abstract:
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).