Geodesic
Branching extremals of the functional of $\lambda$-normed length
Sbornik. Mathematics, Tome 197 (2006) no. 5, pp. 705-726

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Networks on $\lambda$-normed planes are considered, that is, on normed planes for which the unit circle is a regular $2\lambda$-gon. A geometric criterion is given for an arbitrary tree to be extremal on the $\lambda$-normed plane, where $\lambda\ne2,3,4,6$. Problems of $\lambda$-minimal (extremal) realization of an arbitrary network and of convergence of $\lambda$-extremal networks as $\lambda\to\infty$ are also considered. Bibliography: 17 titles. 
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     title = {Branching extremals of the functional of $\lambda$-normed length},
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D. P. Il'yutko. Branching extremals of the functional of $\lambda$-normed length. Sbornik. Mathematics, Tome 197 (2006) no. 5, pp. 705-726. http://geodesic.mathdoc.fr/item/SM_2006_197_5_a2/