Steiner Problem in Gromov-Hausdorff Space: the Case of Finite Metric Spaces

TL;DR

This paper demonstrates that any finite collection of finite metric spaces can be connected by a Steiner minimal tree within Gromov-Hausdorff space, advancing understanding of metric space connectivity.

Contribution

It establishes the existence of Steiner minimal trees connecting finite metric spaces in Gromov-Hausdorff space, a novel result in metric geometry.

Findings

Finite families of finite metric spaces can be connected by Steiner minimal trees.

The result applies within the Gromov-Hausdorff space framework.

This advances the understanding of metric space connectivity and minimal networks.

Abstract

It is shown that each finite family of finite metric spaces, being considered as a subset of Gromov--Hausdorff space, can be connected by a Steiner minimal tree.