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This article is cited in 7 scientific papers (total in 7 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.
Received: 22.05.2001
Citation:
A. O. Ivanov, A. A. Tuzhilin, “Branching geodesics in normed spaces”, Izv. RAN. Ser. Mat., 66:5 (2002), 33–82; Izv. Math., 66:5 (2002), 905–948
Linking options:
https://www.mathnet.ru/eng/im402https://doi.org/10.1070/IM2002v066n05ABEH000402 https://www.mathnet.ru/eng/im/v66/i5/p33
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Abstract page: | 532 | Russian version PDF: | 290 | English version PDF: | 11 | References: | 66 | First page: | 1 |
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