Gyroids of constant mean curvature

Experimental Mathematics

Volumn 6, Issue 1, 1997, Pages 33-50

  Große Brauckmann, Karsten ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031537321     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.1997.10504349     Document Type: Article

References (28)

1. D. M. Anderson, H. T. Davis, J. C. C. Nitsche, and L. E. Scriven, "Periodic surfaces of prescribed mean curvature", Adv. Chem. Phys. 77 (1990), 337-396.
2. M. Athanassenas, "A variational problem for constant mean curvature surfaces with free boundary", J. Reine Angew. Math. 377 (1987), 97-107.
3. K. A. Brakke, "The surface evolver", Experiment. Math. 1:2 (1992), 141-165.
4. K. Brakke, Surface Evolver Manual, Minneapolis: Geometry Center, University of Minnesota, 1994. See http://www.geom.umn.edu/locate/evolver.
5. E. Dubois Violette and B. Pansu (editors), International Workshop on Große-Brauckmann: Gyroids of Constant Mean Curvature 49 Geometry and Interfaces, Les Éditions de Physique, Orsay, 1990. Also J. Physique 51 (1990), no. 23 Colloq. C-7, suppl.
6. S. Förster, A. K. Khandpur, J. Zhao, F. Bates, I. W. Hamley, A. J. Ryan, and W. Bras, "Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder' transition", Macromolecules 27 (1994), 6922-6935.
7. K. Große-Brauckmann, "New surfaces of constant mean curvature", Math. Z. 214:4 (1993), 527-565.
8. K. Große-Brauckmann, "Stable constant mean curvature surfaces minimize area", Pacific J. Math. 175:2 (1996), 527-534.
9. K. Große-Brauckmann, "On gyroid interfaces", J. Colloid and Interface Sc. 187 (1997), 418-428.
10. K. Große-Brauckmann and R. Kusner, "Moduli spaces of embedded constant mean curvature surfaces with few ends and special symmetry", preprint, SFB 256, Universität Bonn, 1996.
11. K. Große-Brauckmann and K. Polthier, "Numerical examples of compact surfaces of constant mean curvature", pp. 23-46 in Elliptic and parabolic methods in geometry, edited by B. Chow et al., A K Peters, Wellesley, MA, 1996.
12. K. Große-Brauckmann and K. Polthier, "Compact constant mean curvature surfaces with low genus", Experiment. Math. 6 (1997), 1-20.
13. K. Große-Brauckmann and K. Polthier, "Constant mean curvature surfaces derived from Delaunay's and Wente's examples", pp. 119-134 in Visualization and mathematics, edited by H.-C. Hege and K. Polthier, Springer, Heidelberg, 1997.
14. K. Große-Brauckmann and M. Wohlgemuth, "The gyroid is embedded and has constant mean curvature companions", Calc. Var. Partial Differential Equations 4:6 (1996), 499-523.
15. D. A. Hajduk, P. E. Harper, S. M. Gruner, C. C. Honeker, G. Kim, E. L. Thomas, and L. J. Fetters, "The gyroid: A new equilibrium morphology in weakly segregated diblock copolymers", Macromolecules 27 (1994), 4063-4075.
16. L. Hsu, R. Kusner, and J. Sullivan, "Minimizing the squared mean curvature integral for surfaces in space forms", Experiment. Math. 1:3 (1992), 190-207.
17. N. Kapouleas, "Complete constant mean curvature surfaces in Euclidean three-space", Ann. of Math. (2) 131:2 (1990), 239-330.
18. H. Karcher, "The triply periodic minimal surfaces of Alan Schoen and their constant mean curvature companions", Manuscripta Math. 64:3 (1989), 291-357.
19. N. Korevaar and R. Kusner, "The global structure of constant mean curvature surfaces", Invent. Math. 114:2 (1993), 311-332.
20. R. Kusner, "Bubbles, conservation laws, and balanced diagrams", pp. 103-108 in Geometric analysis and computer graphics (Berkeley, CA, 1988), Math. Sci. Res. Inst. Publ. 17, Springer, New York, 1991.
21. 3", Ann. of Math. (2) 92 (1970), 335-374.
22. W. H. Meeks III, "The theory of triply periodic minimal surfaces", Indiana Univ. Math. J. 39:3 (1990), 877-936.
23. J. C. C. Nitsche, Lectures on minimal surfaces, Cambridge University Press, Cambridge, 1989. Translated from the German by Jerry M. Feinberg.
24. B. Oberknapp and K. Polthier, "An algorithm for discrete constant mean curvature surfaces", pp. 141-161 in Visualization and mathematics, edited by H.-C. Hege and K. Polthier, Springer, Heidelberg, 1997.
25. M. Ross, "Schwarz' P and D surfaces are stable", Differential Geom. Appl. 2:2 (1992), 179-195.
26. A. H. Schoen, "Infinite periodic minimal surfaces without selfintersections", Technical Note TN D-5541, NASA, 1970.
27. J. M. Sullivan, "VCS: software for computing Voronoi diagrams", 1992. See http://www.geom.umn.edu/-sullivan/software/.
28. E. L. Thomas, D. M. Anderson, C. S. Henkee, and D. Hoffman, "Periodic areaminimizing surfaces in block copolymers", Nature 334 (1988), 598-601.