Geodesic
Directional derivative of the weight of a minimal filling in Riemannian manifolds
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 1 (2015), pp. 15-20 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2015},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a2/}
}
TY  - JOUR
AU  - E. I. Stepanova
TI  - Directional derivative of the weight of a minimal filling in Riemannian manifolds
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2015
SP  - 15
EP  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a2/
LA  - ru
ID  - VMUMM_2015_1_a2
ER  - 
%0 Journal Article
%A E. I. Stepanova
%T Directional derivative of the weight of a minimal filling in Riemannian manifolds
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2015
%P 15-20
%N 1
%U http://geodesic.mathdoc.fr/item/VMUMM_2015_1_a2/
%G ru
%F VMUMM_2015_1_a2
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/

[1] Ivanov A.O., Tuzhilin A.A., “Odnomernaya problema Gromova o minimalnom zapolnenii”, Matem. sb., 203:5 (2012), 65–118 | DOI | MR | Zbl

[2] Garey M.R., Graham R.L., Johnson D.S., “Some NP-complete geometric problems”, Proc. 8th Ann. ACM Symp. on the Theory of Computing, N.Y., 1976, 10–22 | MR | Zbl

[3] Emelichev V.A., Melnikov O.I, Sarvanov V.I., Tyshkevich R.I., Lektsii po teorii grafov, Nauka, M., 1990 | MR

[4] Rubinstein J.H., Thomas D., “A variational approach to the Steiner network problem”, Ann. Oper. Res., 33 (1991), 481–499 | DOI | MR | Zbl

[5] Rubinstein J.H., Thomas D., “The Steiner ratio conjecture for six points”, J. Combin. Theory. Ser. A, 58 (1991), 54–77 | DOI | MR | Zbl

[6] Rubinstein J.H., Thomas D., “The Steiner ratio conjecture for cocircular points”, Discrete and Comput. Geom., 7 (1992), 77–86 | DOI | MR | Zbl

[7] Rubinstein J.H., Thomas D., Weng J.F., “Degree-five Steiner points cannot reduce costs for planar sets”, Networks, 22 (1992), 531–537 | DOI | MR | Zbl

[8] Rubinstein J.H., Thomas D., “Graham's problem on shortest networks for points on a circle”, Algorithmica, 7 (1992), 193–218 | DOI | MR | Zbl

[9] Rubinstein J.H., Thomas D, Wormald N., “Steiner trees for terminals constrained to curves”, SIAM J. Discrete Math., 10 (1997), 1–17 | DOI | MR | Zbl

[10] Ivanov A.O., Tuzhilin A.O., “Differentsialnoe ischislenie na prostranstve minimalnykh derevev Shteinera v rimanovykh mnogoobraziyakh”, Matem. sb., 192:6 (2001), 31–50 | DOI | Zbl

[11] Eremin A.Yu., “Formula vesa minimalnogo zapolneniya konechnogo metricheskogo prostranstva”, Matem. sb., 204:9 (2013), 51–72 | DOI | MR | Zbl