Geodesic
Branching geodesics in normed spaces
Izvestiya. Mathematics , Tome 66 (2002) no. 5, pp. 905-948

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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. 
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     author = {A. O. Ivanov and A. A. Tuzhilin},
     title = {Branching geodesics in normed spaces},
     journal = {Izvestiya. Mathematics },
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     number = {5},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a1/}
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A. O. Ivanov; A. A. Tuzhilin. Branching geodesics in normed spaces. Izvestiya. Mathematics , Tome 66 (2002) no. 5, pp. 905-948. http://geodesic.mathdoc.fr/item/IM2_2002_66_5_a1/