ИСТИНА

The Gromov-Hausdorff distance between metric spaces plays an important role in the Modern Mathematics. The restriction of this distance to the isometry classes of compact metric spaces generates the Gromov-Hausdorff metric space M. In the present talk we discuss some geometrical and variational properties of M. For example, we show that each finite metric space can be isometrically embedded into M, that Steiner minimal trees exist for boundaries consisting of finite metric spaces. Also we demonstrate the relation between Gromov-Hausdorff distance from a finite metric space X to simplices, and the lengths of edges of a minimal spanning tree constructed on X.