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arXiv · 1906.06577

On the Configuration Space of Steiner Minimal Trees

Herbert Edelsbrunner·Nataliya Strelkova
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Abstract

Among other results, we prove the following theorem about Steiner minimal trees in $d$-dimensional Euclidean space: if two finite sets in $\mathbb{R}^d$ 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.

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Herbert Edelsbrunner, Nataliya Strelkova. 2019-06-15. On the Configuration Space of Steiner Minimal Trees. https://arxiv.org/abs/1906.06577

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