Differential calculus on the space of Steiner minimal trees in Riemannian manifoldsстатья
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:It is proved that the length of minimal spanning tree, the length of
Steiner minimal tree, and the Steiner ratio considered as functions on
finite subsets of a connected complete Riemannian manifold have directional
derivatives with respect to any direction. Besides, the derivatives are
calculated and some properties of critical points of these functions are
given. In particular, a geometrical criterion on criticality for Steiner
ratio is obtained. This criterion gives essential restrictions on
geometry of the sets for which the Steiner ratio achieves its minimum,
i.e., their Steiner ratios equal to the one of the ambient space.