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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 5, pp. 159–180, 2016.
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Ivanov, A.O., Tuzhilin, A.A. Analytic Deformations of Minimal Networks. J Math Sci 248, 621–635 (2020). https://doi.org/10.1007/s10958-020-04899-7