Steiner Problem in Gromov-Hausdorff Space: the Case of Finite Metric Spaces
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.
math.MG↗
arXiv subjects
Nadezhda Nikolaeva
Publications and source records attributed to Nadezhda Nikolaeva.
The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic
It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic. In other words, each two points of this space (each two compact metric spaces) can be connected by a geodesic. For finite metric spaces a geodesic is constructed explicitly.
math.MG↗