Triply periodic minimal and constant mean curvature surfaces

Interface Focus

Volumn 2, Issue 5, 2012, Pages 582-588

  Grosse Brauckmann, Karsten ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Curvature; Interface; Minimal surface

Indexed keywords

EID: 84865362640     PISSN: 20428898     EISSN: 20428901     Source Type: Journal    
DOI: 10.1098/rsfs.2011.0096     Document Type: Article

References (12)

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2. Karcher, H. 1989 The triply periodic minimal surfaces of A. Schoen and their constant mean curvature companions. Manuscr. Math. 64, 291-357. doi:10.1007/BF01165824)
3. Grosse-Brauckmann, K. & Wohlgemuth, M. 1996 The gyroid is embedded and has constant mean curvature companions. Calc. Var. 4, 499-523. doi:10.1007/BF01261761)
4. Oberknapp, B. & Polthier, K. 1997 An algorithm for discrete constant mean curvature surfaces. In Visualization and mathematics (eds H.-C. Hege & K. Polthier), pp. 141-161. Heidelberg, Germany: Springer.
5. Korevaar, N., Kusner, R. & Solomon, B. 1989 The structure of complete embedded surfaces with constant mean curvature. J. Differ. Geom. 30, 465-503.
6. Lawson, H. B. 1970 Complete minimal surfaces in S3. Ann. Math. 92, 335-374. doi:10.2307/1970625)
7. Grosse-Brauckmann, K. 1993 New surfaces of constant mean curvature. Math. Zeit. 214, 527-565. doi:10.1007/BF02572424)
8. Anderson, D. M., Davis, H. T., Nitsche, J. C. C. & Scriven, L. E. 1990 Periodic surfaces of prescribed mean curvature. Adv. Chem. Phys. 77, 337-396. doi:10.1002/9780470141267.ch6)
9. Breunig, E. 2011 Systematische Untersuchung dreifach periodischer Flächen konstanter mittlerer Krümmung mit Hilfe der Konjugierten Methode. Diplomarbeit, Darmstadt.
10. Kapouleas, N. 1990 Complete constant mean curvature surfaces in Euclidean three-space. Ann. Math. 131, 239-330. doi:10.2307/1971494)
11. Grosse-Brauckmann, K. 1997 On gyroid interfaces. J. Colloid Interface Sci. 187, 418-428. doi:10.1006/jcis.1996.4720)
12. Bechtloff, N. 2009 Polyhedral surfaces and the Willmore energy. Masters thesis, Darmstadt.