On a maximum principle for minimal surfaces and their integrable discrete counterparts

Journal of Geometry and Physics

Volumn 56, Issue 9, 2006, Pages 1484-1495

  Schief, W K ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Discrete differential geometry; Integrable systems; Minimal surfaces

Indexed keywords

EID: 33745458246     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2005.07.007     Document Type: Article

References (18)

1. Ablowitz M.J., and Segur H. Solitons and the Inverse Scattering Transform (1981), SIAM, Philadelphia
2. Bobenko A., and Pinkall U. Discrete surfaces with constant negative Gaussian curvature and the Hirota equation. J. Diff. Geom. 43 (1996) 527-611
3. Bobenko A., and Pinkall U. Discrete isothermic surfaces. J. Reine Angew. Math. 475 (1996) 187-208
4. Bobenko A.I. Discrete conformal maps and surfaces. In: Clarkson P.A., and Nijhoff F.W. (Eds). Symmetries and Integrability of Difference Equations, London Math. Soc. Lecture Note Series 255 (1999), Cambridge University Press 97-108
5. Bobenko A.I., and Pinkall U. Discretization of surfaces and integrable systems. In: Bobenko A.I., and Seiler R. (Eds). Discrete Integrable Geometry and Physics (1999), Clarendon Press, Oxford 1-58
6. In: Bobenko A.I., and Seiler R. (Eds). Discrete Integrable Geometry and Physics (1999), Clarendon Press, Oxford
7. do Carmo M.P. Differential Geometry of Curves and Surfaces (1976), Prentice-Hall, Englewood Cliffs, NJ
8. Eisenhart L.P. A Treatise on the Differential Geometry of Curves and Surfaces (1960), Dover Publications, New York
9. Hyde S.T. Microstructure of bicontinuous surfactant aggregates. J. Phys. Chem. 93 (1989) 1458-1464
10. Jinnai H., Nishikawa Y., Koga T., and Hashimoto T. Direct observation of three-dimensional bicontinuous structure developed via spinodal decomposition. Macromolecules 28 (1995) 4782-4784
11. Jinnai H., Koga T., Nishikawa Y., Hashimoto T., and Hyde S.T. Curvature determination of spinodal interface in a condensed matter system. Phys. Rev. Lett. 78 (1997) 2248-2251
12. W.E. Lorensen, H.E. Cline, Marching cubes: a high resolution 3D surface construction algorithm, in: Proceedings of the SIGGRAPH'87, Comput. Graphics 21 (1987) 163-169
13. Nishikawa Y., Jinnai H., Koga T., Hashimoto T., and Hyde S.T. Measurements of interfacial curvatures of bicontinuous structure from three-dimensional digital images. 1. A parallel surface method. Langmuir 14 (1998) 1242-1249
14. Rogers C., and Schief W.K. Bäcklund and Darboux Transformations. Geometry and Modern Applications in Soliton Theory. Cambridge Texts in Applied Mathematics (2002), Cambridge University Press
15. Sauer R. Parallelogrammgitter als Modelle pseudosphärischer Flächen. Math. Z. 52 (1950) 611-622
16. Sauer R. Differenzengeometrie (1970), Springer-Verlag, Berlin
17. Schief W.K. On the unification of classical and novel integrable surfaces. II. Difference geometry. Proc. Roy. Soc. London A 459 (2003) 373-391
18. Wunderlich W. Zur Differenzengeometrie der Flächen konstanter negativer Krümmung, Österreich. Akad. Math. -Nat. Kl. S.-B. II 160 (1951) 39-77