Geodesic
Directional derivative of the weight of a minimal filling in Riemannian manifolds
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 15-20

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It is proved that the weight of the minimal filling, the Steiner–Gromov ratio, and the Steiner subratio regarded as functions of finite subsets of a complete connected Riemannian manifold have directional derivatives in all directions. 
@article{VMUMM_2015_1_a2,
     author = {E. I. Stepanova},
     title = {Directional derivative of the weight of a minimal filling in {Riemannian} manifolds},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {15--20},
     publisher = {mathdoc},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a2/}
}
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E. I. Stepanova. Directional derivative of the weight of a minimal filling in Riemannian manifolds. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 15-20. http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a2/