Geodesic
Classification of closed minimal networks on tetrahedra
Sbornik. Mathematics, Tome 82 (1995) no. 1, pp. 101-116 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A complete description is obtained of the closed locally minimal networks on quasiregular tetrahedra. It is shown that on quasiregular tetrahedra the sets of closed locally minimal networks have the same structure as on flat 2-dimensional tori. The paper describes the set of all quasiregular tetrahedra on which there exist closed locally minimal networks of a specified type. In the other direction, it describes the set of all closed minimal networks on a given quasiregular tetrahedron. 
@article{SM_1995_82_1_a4,
     author = {I. V. Ptitsyna},
     title = {Classification of closed minimal networks on tetrahedra},
     journal = {Sbornik. Mathematics},
     pages = {101--116},
     year = {1995},
     volume = {82},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_82_1_a4/}
}
TY  - JOUR
AU  - I. V. Ptitsyna
TI  - Classification of closed minimal networks on tetrahedra
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 101
EP  - 116
VL  - 82
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1995_82_1_a4/
LA  - en
ID  - SM_1995_82_1_a4
ER  - 
%0 Journal Article
%A I. V. Ptitsyna
%T Classification of closed minimal networks on tetrahedra
%J Sbornik. Mathematics
%D 1995
%P 101-116
%V 82
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1995_82_1_a4/
%G en
%F SM_1995_82_1_a4
I. V. Ptitsyna. Classification of closed minimal networks on tetrahedra. Sbornik. Mathematics, Tome 82 (1995) no. 1, pp. 101-116. http://geodesic.mathdoc.fr/item/SM_1995_82_1_a4/

[1] Ivanov A. O., Tuzhilin A. A., “Geometriya minimalnykh setei i odnomernaya problema Plato”, UMN, 47:2 (284) (1992), 53–115 | MR | Zbl

[2] Hwang F. K., Richards D. Winter P., The Steiners Tree Problem, Elsevier Science Publishers (to appear)

[3] Fomenko A. T., Topologicheskie variatsionnye zadachi, Izd-vo MGU, M., 1984 | MR | Zbl

[4] Tuzhilin A. A., Fomenko A. T., Elementy geometrii i topologii minimalnykh poverkhnostei, Nauka, M., 1991 | MR

[5] Ivanov A. O., Ptitsyna I. V., Tuzhilin A. A., “Klassifikatsiya zamknutykh minimalnykh setei na ploskikh dvumernykh torakh”, Matem. sb., 183:12 (1992), 3–44 | MR | Zbl