Geodesic
Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds
Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 1049-1072

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In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular $n$-gons with $n\geqslant 7$ their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles.
Keywords: minimal networks. 
@article{SM_2017_208_7_a5,
     author = {V. M. Chikin},
     title = {Steiner minimal trees in small neighbourhoods of points in {Riemannian} manifolds},
     journal = {Sbornik. Mathematics},
     pages = {1049--1072},
     publisher = {mathdoc},
     volume = {208},
     number = {7},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_7_a5/}
}
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V. M. Chikin. Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds. Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 1049-1072. http://geodesic.mathdoc.fr/item/SM_2017_208_7_a5/