ИСТИНА

This lecture is devoted to geometry optimal connections networks in metric spaces especially minimal fillings, and to the Gromov-Hausdorff distance that measures “difference” between two metric spaces. If metric spaces are isometric then the distance vanishes, that is why it is naturally to consider the distance on isometry classes of metric spaces. In the case when the metric spaces in consideration are compact, this distance is a metric, and the corresponding “hyperspace” is called Gromov-Hausdorff space. Our talk mainly devoted to description of geometry of the Gromov- Hausdorff space.