This article is cited in 8 papers

Locally Minimal Trees in $n$-Normed Spaces

D. P. Il'yutko

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 514.77+519.711.72+517.982.22

Received: 03.09.2001
Revised: 21.04.2003

DOI: 10.4213/mzm298

 English version: Mathematical Notes, 2003, 74:5, 619–629

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