Geodesic
Steiner Ratio for Manifolds
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 387-395.

Voir la notice de l'article provenant de la source Math-Net.Ru

The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As a corollary, the Steiner ratio for flat tori, flat Klein bottles, and projective plane of constant positive curvature are computed. 
@article{MZM_2003_74_3_a6,
     author = {A. O. Ivanov and A. A. Tuzhilin and D. Cieslik},
     title = {Steiner {Ratio} for {Manifolds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {387--395},
     publisher = {mathdoc},
     volume = {74},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a6/}
}
TY  - JOUR
AU  - A. O. Ivanov
AU  - A. A. Tuzhilin
AU  - D. Cieslik
TI  - Steiner Ratio for Manifolds
JO  - Matematičeskie zametki
PY  - 2003
SP  - 387
EP  - 395
VL  - 74
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a6/
LA  - ru
ID  - MZM_2003_74_3_a6
ER  - 
%0 Journal Article
%A A. O. Ivanov
%A A. A. Tuzhilin
%A D. Cieslik
%T Steiner Ratio for Manifolds
%J Matematičeskie zametki
%D 2003
%P 387-395
%V 74
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a6/
%G ru
%F MZM_2003_74_3_a6
A. O. Ivanov; A. A. Tuzhilin; D. Cieslik. Steiner Ratio for Manifolds. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 387-395. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a6/

[1] Du D. Z., Hwang F. K., “A proof of Gilbert–Pollak Conjecture on the Steiner ratio”, Algorithmica, 7 (1992), 121–135 | DOI | MR | Zbl

[2] Gilbert E. N., Pollak H. O., “Steiner minimal trees”, SIAM J. Appl. Math., 16:1 (1968), 1–29 | DOI | MR | Zbl

[3] Cieslik D., Steiner Minimal Trees, Kluwer Academic Publishers, 1998

[4] Rubinstein J. H., Weng J. F., “Compression theorems and Steiner ratios on spheres”, J. Combin. Optimization, 1 (1997), 67–78 | DOI | MR | Zbl

[5] Ivanov A. O., Tuzhilin A. A., Minimal Networks. The Steiner Problem and Its Generalizations, CRC Press, N.W., Boca Raton, Florida, 1994 | Zbl

[6] Ivanov A. O., Tuzhilin A. A., Branching Solutions of One-Dimensional Variational Problems, World Publisher Press, 2000 (to appear)

[7] Hwang F. K., Richards D., Winter P., The Steiners Tree Problem, Elsevier Science Publishers, 1992