Abstract
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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Ivanov, A.O., Van, L.H. & Tuzhilin, A.A. Nontrivial Critical Networks. Singularities of Lagrangians and a Criterion for Criticality. Mathematical Notes 69, 514–526 (2001). https://doi.org/10.1023/A:1010260230867
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DOI: https://doi.org/10.1023/A:1010260230867