Geodesic
Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality
Matematičeskie zametki, Tome 69 (2001) no. 4, pp. 566-580

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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. 
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     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},
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     year = {2001},
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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/