This article is cited in 8 papers

Branching geodesics in normed spaces

A. O. Ivanov, A. A. Tuzhilin

M. V. Lomonosov Moscow State University

Abstract: We study branching extremals of length functionals on normed spaces. This is a natural generalization of the Steiner problem in normed spaces. We obtain criteria for a network to be extremal under deformations that preserve the topology of networks as well as under deformations with splitting. We discuss the connection between locally shortest networks and extremal networks. In the important particular case of the Manhattan plane, we get a criterion for a locally shortest network to be extremal.

UDC: 514.77+519.176

MSC: 05C35, 90C35, 68R10

Received: 22.05.2001

DOI: 10.4213/im402

 English version: Izvestiya: Mathematics, 2002, 66:5, 905–948

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