On the configuration space of Steiner minimal trees
Herbert Edelsbrunner, Nataliya Pavlovna Strelkova · Russian Mathematical Surveys · 2012
Among other results, we prove the following theorem about Steiner minimal trees in d-dimensional Euclidean space: if two finite sets in R d have unique and combinatorially equivalent Steiner minimal trees, then there is a homotopy between the two sets that maintains the uniqueness and the combinatorial structure of the Steiner minimal tree throughout the homotopy.