Geodesic
Analytic deformations of minimal networks
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 159-180.

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The behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of the boundary set guarantees preservation of the network type for minimal spanning trees, minimal fillings, and so-called stable shortest trees in the Euclidean space. 
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A. O. Ivanov; A. A. Tuzhilin. Analytic deformations of minimal networks. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 5, pp. 159-180. http://geodesic.mathdoc.fr/item/FPM_2016_21_5_a6/

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