Geodesic
Locally Minimal Trees in $n$-Normed Spaces
Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 656-668.

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The locally minimal trees in normed spaces $({\mathbb R}^2,\rho)$, where the unit circle $\Sigma=\{x\in{\mathbb R}^2\mid{\rho}(x)=1\}$ in the norm $\rho$ coincides with the regular $m$-gon ($m = 2n$) inscribed in the Euclidean unit circle $S^1$, are completely classified. 
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D. P. Il'yutko. Locally Minimal Trees in $n$-Normed Spaces. Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 656-668. http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a1/

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