Branched coverings and Steiner ratio
Copyright policy )Branched coverings and Steiner ratio
AbstractFor 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 at its vertex is also equal to the Steiner ratio of the Euclidean plane.
- University of Technology Russian Federation
- Lomonosov Moscow State University Russian Federation
- Bauman Moscow State Technical University Russian Federation
branched covering, Mathematics - Metric Geometry, flat cone, FOS: Mathematics, Metric Geometry (math.MG), Programming involving graphs or networks, locally isometric covering, Steiner ratio, isosceles tetrahedron
branched covering, Mathematics - Metric Geometry, flat cone, FOS: Mathematics, Metric Geometry (math.MG), Programming involving graphs or networks, locally isometric covering, Steiner ratio, isosceles tetrahedron
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