ИСТИНА

The present talk devoted to a new eld in the theory of variational problems with branching extremals, the investigation of one-dimensional minimal llings of nite metric spaces. On the one hand, this problem is a one-dimensional version of a gen- eralization of Gromov's minimal llings problem to the case of stratied manifolds. On the other hand, this problem can be considered as a generalization of the Steiner problem on the description of a shortest network joining a given set of terminals. We shall discuss the recent progress in this theory.