ИСТИНА

It is known that any local minimal network on the Euclidean plane is extremal, but the same fact is not true for any normed plane. The first part of our talk is devoted to extremal networks on normed planes. The famous Maxwell formula provides a tool to calculate the length a local minimal tree in the Euclidean plane. An interesting question is to find a generalization of this formula for the case of normed spaces. It turns out that Maxwell formula becomes invalid for local minimal trees in the case of non-smooth normed spaces. In the second part of our talk we present an analogue of Maxwell formula for extremal trees in an arbitrary normed space.