Geodesic
Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 48-51 
E. I. Stepanova. Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2016), pp. 48-51. http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a8/
@article{VMUMM_2016_2_a8,
     author = {E. I. Stepanova},
     title = {Bifurcations of {Steiner} minimal trees and minimal fillings for non-convex four-point boundaries and {Steiner} subratio for the {Euclidean} plane},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {48--51},
     year = {2016},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a8/}
}
TY  - JOUR
AU  - E. I. Stepanova
TI  - Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 48
EP  - 51
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a8/
LA  - ru
ID  - VMUMM_2016_2_a8
ER  - 
%0 Journal Article
%A E. I. Stepanova
%T Bifurcations of Steiner minimal trees and minimal fillings for non-convex four-point boundaries and Steiner subratio for the Euclidean plane
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 48-51
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_2_a8/
%G ru
%F VMUMM_2016_2_a8

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

Bifurcation diagrams for topologies of Steiner minimal trees and minimal fillings for nonconvex four-pointed boundaries are constructed. Using this issue, the four-pointed Steiner subratio of the Euclidean plane is recieved. All configurations for which it is obtained are found.

[1] Ivanov A.O., Tuzhilin A.A., Teoriya ekstremalnykh setei, Izd-vo In-ta kompyuternykh issledovanii, M.–Izhevsk, 2003 | MR

[2] Karpunin G.A., “Analog teorii Morsa dlya ploskikh lineinykh setei i obobschennaya problema Shteinera”, Matem. sb., 191:5 (2000), 64–90 | DOI | MR | Zbl

[3] Ivanov A.O., Tuzhilin A.A., Tsislik D., “Otnoshenie Shteinera dlya mnogoobrazii”, Matem. zametki, 74:3 (2003), 387–395 | DOI | MR | Zbl

[4] Ilyutko D.P., “Razvetvlennye ekstremali funktsionala $\lambda$-normirovannoi dliny”, Matem. sb., 197:5 (2006), 75–98 | DOI | MR | Zbl

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

[6] Cieslik D., The Steiner ratio of metric spaces, A report. Preprintreihe Mathematik, 2010 | MR

[7] Yiu P., Introduction to the geometry of the triangle, Florida Atlantic University Lect. Notes, 2001

[8] Akopyan A.V., Geometriya v kartinkakh, MTsNMO, M., 2011

[9] Kimberling C., Encyclopedia of triangle centers, http://faculty.evansville.edu/ck6/encyclopedia/ETC.html

[10] Ovsyannikov Z.N., “Subotnoshenie Shteinera dlya pyati tochek na ploskosti i chetyrekh tochek v prostranstve”, Fund. i prikl. matem., 18:2 (2013), 167–179