Geodesic
Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality
Matematičeskie zametki, Tome 69 (2001) no. 4, pp. 566-580 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We single out the class of so-called quasiregular Lagrangians, which have singularities on the zero section of the cotangent bundle to the manifold on which extremal networks are considered. A criterion for a network to be extremal is proved for such Lagrangians: the Euler–Lagrange equations must be satisfied on each edge, and some matching conditions must be valid at the vertices. 
@article{MZM_2001_69_4_a4,
     author = {A. O. Ivanov and A. A. Tuzhilin and L\^e H\^ong V\^an},
     title = {Nontrivial {Critical} {Networks.} {Singularities} of {Lagrangians} and a {Criterion} for {Criticality}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {566--580},
     year = {2001},
     volume = {69},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_4_a4/}
}
TY  - JOUR
AU  - A. O. Ivanov
AU  - A. A. Tuzhilin
AU  - Lê Hông Vân
TI  - Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality
JO  - Matematičeskie zametki
PY  - 2001
SP  - 566
EP  - 580
VL  - 69
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_4_a4/
LA  - ru
ID  - MZM_2001_69_4_a4
ER  - 
%0 Journal Article
%A A. O. Ivanov
%A A. A. Tuzhilin
%A Lê Hông Vân
%T Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality
%J Matematičeskie zametki
%D 2001
%P 566-580
%V 69
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_4_a4/
%G ru
%F MZM_2001_69_4_a4
A. O. Ivanov; A. A. Tuzhilin; Lê Hông Vân. Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality. Matematičeskie zametki, Tome 69 (2001) no. 4, pp. 566-580. http://geodesic.mathdoc.fr/item/MZM_2001_69_4_a4/

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

[2] Dubrovin B. A., Novikov S. P., Fomenko A. T., Sovremennaya geometriya, Nauka, M., 1986

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

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