2016/05/03 by Alexander Ivanov, Ivanov, Alexander, Alexey Avgustinovich Tuzhilin +1
Mathematics · #51F99 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1605.01094
openalex publication_date 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we investigate the metric space \cal M consisting of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We show that for any finite subset M from a sufficiently small neighborhood of a generic finite metric space, providing M consists of finite metric spaces with the same number of points, each Steiner minimal tree in \cal M connecting M is a minimal filling for M. As a consequence, we prove that the both Steiner ratio and Gromov-Steiner ratio of \cal M are equal to 1/2.