Geodesic
Classification of metric spaces whose Steiner--Gromov ratio is equal to one
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 181-189

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Several equivalent conditions for the Steiner–Gromov ratio of a metric space to be equal to one are stated, i.e., conditions for each minimal spanning tree in any finite subset of a given metric space to be both a shortest tree and a minimal filling. A complete classification of such spaces is obtained. 
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     author = {A. S. Pahkomova},
     title = {Classification of metric spaces whose {Steiner--Gromov} ratio is equal to one},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
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     publisher = {mathdoc},
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     number = {5},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a7/}
}
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A. S. Pahkomova. Classification of metric spaces whose Steiner--Gromov ratio is equal to one. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 181-189. http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a7/