2015/06/12 by Alexander Ivanov, A. A. Tuzhilin · 1 citation
Computer Science · Engineering · Mathematics · #Computational Geometry and Mesh Generation #Advanced Materials and Mechanics #Point processes and geometric inequalities #Isosceles triangle #Steiner tree problem #Combinatorics #Mathematics #Euclidean geometry #Tetrahedron #Vertex (graph theory) #Steiner system #Minimal surface #Euclidean space #Geometry #Graph
paper · pdf · doi:10.1111/itor.12182
openalex publication_date 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27
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 at its vertex is also equal to the Steiner ratio of the Euclidean plane.