Uniqueness of Steiner minimal trees on boundaries in general positionстатья
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Аннотация:In the present work the following result is proved: there exists an open
everywhere dense subset $U\ss\R^{2n}$, such that each $P\in U$ (considered
as enumerated subset of the standard Euclidean plane $\R^2$) is spanned by
unique Steiner minimal tree, i.e\. non-degenerated shortest network.
Besides, several interesting corollaries are obtained. In particular, it
is proved that any planar Steiner tree is planar equivalent to a Steiner
minimal tree.