2014/12/17 by Ivanov, Alexandr, Alexey Avgustinovich Tuzhilin, Tuzhilin, Alexey
Computer Science · Mathematics · #Computational Geometry and Mesh Generation #FOS: Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1412.5433
openalex publication_date 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 2π/k at its vertex is also equal to the Steiner ratio of the Euclidean plane.