Bibliography
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.)
L. Barbosa and G. Colares,Examples of Minimal Surfaces, to appear in Springer Lecture Notes series.
J-P. Bourguignon, H. B. Lawson and C. Margenn, “Les surfaces minimales,”Pour la Science, January 1986.
S. Hildebrandt and A. J. Tromba,The Mathematics of Optimal Form, Scientific American Library, 1985, W. H. Freeman, New York.
D. Hoffman,The discovery of new embedded minimal surfaces: elliptic functions; symmetry; computer graphics, Proceedings of the Berlin Conference on Global Differential Geometry, Berlin, June 1984.
D. Hoffman,The construction of families of embedded minimal surfaces, to appear in the Proceddings of the Stanford Conference on Variational Methods for Free Surface Interfaces, September 1985.
D. Hoffman and W. Meeks III, “Complete embedded minimal surfaces of finite total curvature,”Bull. A.M.S., January 1985, 134-136.
D. Hoffman and W. Meeks III, “A complete embedded minimal surface with genus one, three ends and finite total curvature,”Journal of Differential Geometry, March 1985.
D. Hoffman and W. Meeks III,The global theory of embedded minimal surfaces, to appear.
L. Jorge and W. Meeks III, “The topology of complete minimal surfaces of finite total Gaussian curvature,”Topology, 22 No. 2, 1983, 203–221.
H. B. Lawson Jr,Lectures on Minimal Submanifolds, Publish or Perish Press, Berkeley, 1971.
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.
R. Osserman, “Global properties of minimal surfaces in E3 and En,”Ann. of Math., 80 (1984), 340–364.
R. Osserman,A Survey of Minimal Surfaces, 2d Edition, Dover Publications, New York, 1986.
R. Schoen, “Uniqueness, symmetry, and embeddedness of minimal surfaces,”J. Dif. Geom. 18, 1983, 791–809.
I. Peterson, “Three Bites in a Doughnut,”Science News 127, No. 11, 16 March 1985.
Dr. Crypton, “Shapes that eluded discovery,”Science Digest, April 1986.
S. Papert,Mindstorms; Children, Computers, and Powerful Ideas, Basic Books, New York, 1980.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hoffman, D., Matisse, H. The computer-aided discovery of new embedded minimal surfaces. The Mathematical Intelligencer 9, 8–21 (1987). https://doi.org/10.1007/BF03023947
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03023947