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The computer-aided discovery of new embedded minimal surfaces. (English) Zbl 0616.53007
This is a report on some recent developments in the theory of minimal surfaces. After some historical remarks the construction of the author’s and B. Meeks’ examples of complete embedded minimal surfaces of finite topological type is described, beginning with C. Costa’s example from 1984. The use of computer graphics for the construction of the examples is exhibited. The mathematical background has been published in several recent papers.
Reviewer: Bernd Wegner

MSC:
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
53-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry
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[1] C. Costa, ”Imersões minimas completas em R3 de gênero um e curvatura total finita,” Doctoral thesis, IMPA, Rio de Janeiro, Brasil, 1982. (Example of a complete minimal immersion in R3 of genus one and three embedded ends.Bull. Soc. Bras. Mat., 15 [1984] 47–54.) · Zbl 0613.53002 · doi:10.1007/BF02584707
[2] L. Barbosa and G. Colares,Examples of Minimal Surfaces, to appear in Springer Lecture Notes series. · Zbl 0609.53001
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[10] L. Jorge and W. Meeks III, ”The topology of complete minimal surfaces of finite total Gaussian curvature,”Topology, 22 No. 2, 1983, 203–221. · Zbl 0517.53008 · doi:10.1016/0040-9383(83)90032-0
[11] H. B. Lawson Jr,Lectures on Minimal Submanifolds, Publish or Perish Press, Berkeley, 1971.
[12] J. C. C. Nitsche,Minimal surfaces and partial differential equations, inStudies in Partial Differential Equations, Walter Littman, ed., MAA Studies in Mathematics, Vol. 23, Mathematical Association of America, 1982. · Zbl 0533.53003
[13] R. Osserman, ”Global properties of minimal surfaces in E3 and En,”Ann. of Math., 80 (1984), 340–364. · Zbl 0134.38502 · doi:10.2307/1970396
[14] R. Osserman,A Survey of Minimal Surfaces, 2d Edition, Dover Publications, New York, 1986. · Zbl 0209.52901
[15] R. Schoen, ”Uniqueness, symmetry, and embeddedness of minimal surfaces,”J. Dif. Geom. 18, 1983, 791–809. · Zbl 0575.53037
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