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References
D. Cieslik, Steiner Minimal Trees, Kluwer Academic Publishers, Dordrecht-Boston-London, 1998.
Dao Chong Thi, A. T. Fomenko, Minimal Surfaces and Plateau Problem, Nauka, Moscow, 1987 (in Russian). (Engl. translation Amer. Math. soc., Providence, RI, 1991.)
B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry, Nauka, Moscow, 1986. English translation: Part 1, GTM 93, 1984; Part 2, GTM 104, 1985, Springer-Verlag, New York.
M. Emmer, Bolle di sapone: un viaggio tra matematica, arte e fantasia, La Nuova Italia, Firenze, 1991.
M. Emmer, Soap Bubbles in art and science, M. Emmer, ed., The Visual Mind, MIT press, 1993.
M. Emmer, Soap Bubbles, video, english version, 27 minutes, Rome (1984).
A. T. Fomenko, and A. A. Tuzhilin, Elements of geometry and topology of minimal surfaces in three-dimensional space, Translations of Math. Monographs, AMS, v. 93, 1992.
R. L. Francis, A note on the optimum location of new machines in existing plant layouts, J. Indust. Engrg., v. 14, pp. 57–59, 1963.
M. R. Garey, and D. S. Johnson, The Rectilinear Steiner Problem is NP-Complete, SIAM J. Appl. Math., v. 32, pp. 826–834, 1977.
M. Hanan, On Steiner’s Problem with Rectilinear Distance, SIAM J. Appl. Math., v. 14, pp. 255–265, 1966.
S. Hildebrandt, and A. Tromba, The Parsimonious Universe, Springer-Verlag, New York, 1996.
F. K. Hwang, On Steiner minimal trees with rectilinear distance, SIAM J. of Appl. Math., v. 30, pp. 104–114, 1976.
F. K. Hwang, D. Richards, and P. Winter, The Steiners Tree Problem, Elsevier Science Publishers, 1992.
A. O. Ivanov, and A. A. Tuzhilin, Minimal Networks. The Steiner Problem and Its Generalizations, CRC Press, N.W., Boca Raton, Florida, 1994.
A. O. Ivanov, and A. A. Tuzhilin, Branching Solutions to One-Dimensional Variational Problems, World Scientific Publ., 2001.
V. Jarnik, and M. Kössler, O minimalnich grafeth obeahujicich n danijch bodu, Cas. Pest. Mat. a Fys., v. 63, pp. 223–235, 1934.
L. S. Polak, Variational principals in mechanics, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1959 (in Russian).
J. E. Taylor, The structure of singularities in soap-bubble-like and soapfilm-like minimal surfaces, Ann. Math., v. 103, pp. 489–539, 1976.
J. A. Thorpe, Elementary topics in differential geometry, Springer-Verlag, New York, 1979.
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Fomenko, A.T., Ivanov, A.O., Tuzhilin, A.A. (2005). Visual Topology and Variational Problems on Two-Dimensional Surfaces. In: Emmer, M. (eds) Mathematics and Culture II. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26443-4_10
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DOI: https://doi.org/10.1007/3-540-26443-4_10
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