Geodesic
A Continuity Criterion for Steiner-Type Ratios in the Gromov--Hausdorff Space
Matematičeskie zametki, Tome 96 (2014) no. 1, pp. 126-137

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A criterion for the continuity of the Steiner ratio, the Steiner subratio, and the Steiner–Gromov ratio in the space of all compact metric spaces with the Gromov–Hausdorff metric is obtained. It is also proved that these functions are upper semicontinuous.
Keywords: Steiner ratio, Steiner subratio, Steiner–Gromov ratio, Gromov–Hausdorff metric, Gromov–Hausdorff space, minimal filling, Steiner minimal tree. 
@article{MZM_2014_96_1_a10,
     author = {A. C. Pahkomova},
     title = {A {Continuity} {Criterion} for {Steiner-Type} {Ratios} in the {Gromov--Hausdorff} {Space}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {126--137},
     publisher = {mathdoc},
     volume = {96},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a10/}
}
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A. C. Pahkomova. A Continuity Criterion for Steiner-Type Ratios in the Gromov--Hausdorff Space. Matematičeskie zametki, Tome 96 (2014) no. 1, pp. 126-137. http://geodesic.mathdoc.fr/item/MZM_2014_96_1_a10/