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arXiv · 1412.5433

Branched Coverings and Steiner Ratio

Alexandr Ivanov·Alexey Tuzhilin
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Abstract

For a branched locally isometric covering of metric spaces with intrinsic metrics, it is proved that the Steiner ratio of the base is not less than the Steiner ratio of the total space of the covering. As applications, it is shown that the Steiner ratio of the surface of an isosceles tetrahedron is equal to the Steiner ratio of the Euclidean plane, and that the Steiner ratio of a flat cone with angle of $2\pi/k$ at its vertex is also equal to the Steiner ratio of the Euclidean plane.

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Alexandr Ivanov, Alexey Tuzhilin. 2014-12-17. Branched Coverings and Steiner Ratio. https://arxiv.org/abs/1412.5433

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