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Computer graphics tools for the study of minimal surfaces
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Communications of the ACM archive
Volume 31 ,  Issue 6  (June 1988) table of contents
Pages: 648 - 661  
Year of Publication: 1988
ISSN:0001-0782
Authors
M. J. Callahan  Department of Mathematics, Science Center, Harvard University, 1 Oxford St., Cambridge, MA
D. Hoffman  Department of Mathematics and Statistics, Lederle Graduate Center, University of Massachusetts at Amherst, MA
J. T. Hoffman
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 5,   Downloads (12 Months): 34,   Citation Count: 3
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ABSTRACT

Recent research indicates machine computation and mathematical theory have proceeded hand in hand and have proved to be of great benefit to one another.


REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
Anderson, D. Studies in the microstructure of microemulsions. Ph,D. thesis, Dept. of Chemical Engineering, Univ. of Minnesota, Minneapolis, Minn. June 1986.
 
2
Anderson, D., and Thomas, E.L. Microdomain morphology of star copolymers in the strong-segregation limit. Dept. of Polymer Science, Univ. of Massachusetts, Amherst.
 
3
Callahan, M., Hoffman, D., and Meeks, W., III. Embedded minimal surfaces with an infinite number of ends. Geometry, C, omputation and Graphics Preprint Series, Department of Mathematics, Univer- - sity of Massachusetts, Amherst, Mass., Sept. 1987.
 
4
Callahan, M., Hoffman, D., and Meeks, W., III. Embedded minimal surfaces with four ends. Geometry, Computation and Graphics Preprint Series, Department of Mathematics, University of Massachusetts, Amherst, Mass., in preparation.
 
5
Costa, C. Example of a complete minimal immersion :.n R3 of genus one and three embedded ends. Bull. Soc. Bras. Mat. 15 (1984), 47-54.
 
6
Crypton. Shapes that eluded discovery. Sci. Dig. 94, 4 (Apr. 1986), 50-55.
 
7
Hoffman, D. The computer-aided discovery of new embedded minimal surfaces. Math. Intell. 9, 3 (July 1987), 8-21.
 
8
Hoffman, D. The construction of families of embedded minimal surfaces. In Variational Methods for Free Surface Interfaces, P. Concus and R. Finn, Ed. Springer-Verlag, New York, 1987, pp. 25-36.
 
9
Hoffman, D., and Meeks, W., III. Complete embedded minimal surfaces of finite total curvature. Bull. A. M. S. 12, 1 (Jan. 1985), 134-136.
 
10
Hoffman, D., and Meeks, W., III. A complete embedded minimal surface with genus one, three ends and finite total curvature. J. Differ. Geom. 21 (Mar. 1985), 109-t27.
 
11
11. Hoffman, D., and Meeks, W., III. The global theory of embedded minimal surfaces. Geometry, Computation and Graphics Preprint Series, Department of Mathematics, University of Massachusetts, Amherst, Mass., Nov. 1987.
 
12
Hoffman, D., and Meeks, W., III. One-parameter families of embedded minimal surfaces. Geometry, Computation and Graphics Preprint Series, Department of Mathematics, University of Massachusetts, Amherst, Mass., April 1988.
 
13
Hoffman, D., and Meeks, W., III. Properties of properly embedded minimal surfaces of finite total curvature. Bull. A. M. S. 17, 2. To be published.
 
14
Hopf, H. Differential Geometry in the Large. Lecture Notes in Mathematics, vol. 1000. Springer-Verlag, New York, 1984.
 
15
Karcher, H. Families of triply-periodic surfaces of constant mean curvature. Preprint, SFB, Univ. of Bonn, Bonn, Germany. April 1987.
 
16
Osserman, R. A Survey of Minimal Surfaces. 2nd ed. Dover Publications, New York, 1986.
 
17
Rotman, D. A new look in block copolymers. Ind. Chem. News 7, 11 (Nov. 1986), 4-5.
 
18
Schoen, A. Infinite periodic minimaI surfaces without self-intersections. Tech. Note D-5541, NASA, Cambridge, Mass., May 1970.
 
19
Scriven, L.E. Bicontinuous structures. Nature 263, 5573 (Sept. 1976), 123.
 
20
Stewart, I. One hundred per cent proof. Nature 324, (Dec. 1986), 4O6-4O7.
 
21
Thomas, E.L., Alward, D.B., Kinning, D.J., Martin, D.C., Jr., Handlin, D.L., and Fetters, L.J. Ordered bicontinuous double-diamond structure of star block copolymers: A new equilibrium microdomain morphology. Macromolecules 19, (1986), 2197-2202.
 
22
Wente, H. Counterexampte to a conjecture of H. Hopf. Pac. }. 121 (1986), 193-243.


Collaborative Colleagues:
M. J. Callahan: colleagues
D. Hoffman: colleagues
J. T. Hoffman: colleagues