The morphology of vesicles of higher topological genus: Conformal degeneracy and conformal modes

Journal de Physique II

Volumn 6, Issue 12, 1996, Pages 1797-1824

  Jülicher, Frank ^a,b,c  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b SIMON FRASER UNIVERSITY   (Canada)

^c INSTITUT CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; LIQUID MEMBRANES; MATHEMATICAL MODELS; MORPHOLOGY; PHASE DIAGRAMS; SURFACE STRUCTURE; TOPOLOGY;

CONFORMAL DIFFUSION; CONFORMAL MODES; LIPID VESICLES; VESICLE TOPOLOGY; WILMORE SURFACES;

LIPIDS;

EID: 0030412664     PISSN: 11554312     EISSN: None     Source Type: Journal    
DOI: 10.1051/jp2:1996161     Document Type: Article

References (49)

1. Lipowsky R., Nature 349 (1991) 475.
2. Bloom M., Evans E. and Mouritsen O., Q. Rev. Biophys. 24 (1991) 293.
3. Berndl K., et al., Europhys. Lett. 13 (1990) 659.
4. Käs J. and Sackmann E., Biophys. J. 60 (1991) 825.
5. Evans E. and Rawicz W., Phys. Rev. Lett. 64 (1990) 2094.
6. Wiese W., Harbich W. and Helfrich W., J. Phys.: Cond. Matter 4 (1992) 1647.
7. Helfrich W., Z. Naturforsch. 28c (1973) 693.
8. Evans E., Biophys. J. 14 (1974) 923.
9. Deuling H. and Helfrich W., J. Phys. France 37 (1976) 1335.
10. Svetina S. and Zeks B., Eur. Biophys. J. 17 (1989) 101.
11. Seifert U., Berndl K. and Lipowsky R., Phys. Rev. A 44 (1991) 1182.
12. Miao L., et al., Phys. Rev. A 43 (1991) 6843.
13. Miao L., Seifert U., Wortis M. and Döbereiner H.-G., Phys. Rev. E 49 (1994) 5389.
14. Wintz W., Döbereiner H.-G. and Seifert U., Europhys. Lett. 33 (1996) 403.
15. Mutz M. and Bensimon D., Phys. Rev. A 43 (1991) 4525.
16. Fourcade B., Mutz M. and Bensimon D., Phys. Rev. Lett. 68 (1992) 2551.
17. Michalet X. and Bensimon D., J. Phys. II France 5 (1995) 263.
18. Michalet X., Bensimon D. and Fourcade B., Phys. Rev. Lett. 72 (1994) 168.
19. Michalet X. and Bensimon D., Science 269 (1995) 666.
20. Willmore T., Total curvature in Riemannian geometry (Ellis Horwood, Chicester, 1982).
21. Duplantier B., Physica A 168 (1990) 179.
22. Duplantier B., Goldstein R., Romero-Rochin V. and Pesci A., Phys. Rev. Lett. 65 (1990) 508.
23. Seifert U., Phys. Rev. Lett. 66 (1991) 2404.
24. Seifert U., J. Phys. A: Math. Gen. 24 (1991) L573.
25. Fourcade B., J. Phys. II France 2 (1992) 1705.
26. Jülicher F., Seifert U. and Lipowsky R., J. Phys. II France 3 (1993) 1681.
27. Jülicher F., Seifert U. and Lipowsky R., Phys. Rev. Lett. 71 (1993) 452.
28. Pinkall U. and Sterling I., Math. Intelligencer 9 (1987) 38.
29. Hsu L., Kusner R. and Sullivan J., Experimental Math. 1 (1992) 191.
30. Kusner R., Pacific J. Math. 138 (1989) 317.
31. Thomsen G., Abh. Math. Sem. Univ. Hamburg 3 (1923) 31.
32. Blaschke W., Vorlesungen über Differentialgeometrie (Springer, Berlin, 1929).
33. Lawson H., Ann. Math. 92 (1970) 335.
34. Karcher H., Pinkall U. and Sterling I., J. Differential Geometry 28 (1988) 169.
35. Willmore T., Anal. Scient. ale Univ. Iasi (Sect. Ia) 11 (1965) 493.
36. Note that definition (9) differs from those used in references [24,26] by a minus sign.
37. Ashcroft N. and Mermin N., Solid State Physics (CBS Publishing Asia Ltd., Philadelphia, 1976).
38. This "handle" has two holes since the limit shape is of topolqgical genus g = 2.
39. Note that no additional Willmore surfaces can be generated by using inversion centers located in the exterior of L. This fact follows from the inversion symmetry of L.
40. The limit |a| → ∞ leads to the Lawson surface which is not part of any conformal mode.
41. Brochard F. and Lennon J., J. Phys. France 36 (1975) 1035.
42. Evans E. and Needham D., J. Phys. Chem. 91 (1987) 4219.
43. Duwe H., Kas J. and Sackmann E., J. Phys. France 51 (1990) 945.
44. Mutz M. and Helfrich W., J. Phys. France 51 (1990) 991.
45. 2h-symmetry corresponds to a two-fold axis and an additional mirror plane perpendicular to this axis.).
46. do Carmo M., Differential Geometry of Curves and Surfaces (Prentice-Hall, New Jersey, 1976).
47. Nitsche J., Lectures on minimal surfaces (Cambridge University Press, Cambridge, 1989).
48. 2+1+4δH̃/δε̃ = 0, is also a stationary solution of the Willmore functional with δG = 0. However, no surface with δG = 0 is known which does not correspond to a minimal surface [28].
49. Spivak M., Differential Geometry (Publish or Perish, Houston, 1979).