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Numéro
J. Phys. II France
Volume 6, Numéro 12, December 1996
Page(s) 1797 - 1824
DOI https://doi.org/10.1051/jp2:1996161
References of J. Phys. II France 6 1797-1824
  1. Lipowsky R., Nature 349 (1991) 475 [CrossRef] [PubMed].
  2. Bloom M., Evans E. and Mouritsen O., Q. Rev. Biophys. 24 (1991) 293 [PubMed].
  3. Berndl K., et al., Europhys. Lett. 13 (1990) 659 [CrossRef].
  4. K $\ddot{\textrm{a}}$s J. and Sackmann E., Biophys. J. 60 (1991) 825 [PubMed].
  5. Evans E. and Rawicz W., Phys. Rev. Lett. 64 (1990) 2094 [CrossRef] [PubMed].
  6. Wiese W., Harbich W. and Helfrich W., J. Phys.: Cond. Matter 4 (1992) 1647 [CrossRef].
  7. Helfrich W., Z. Naturforsch. 28c (1973) 693.
  8. Evans E., Biophys. J. 14 (1974) 923 [PubMed].
  9. Deuling H. and Helfrich W., J. Phys. France 37 (1976) 1335 [CrossRef] [EDP Sciences].
  10. Svetina S. and Zeks B., Eur. Biophys. J. 17 (1989) 101 [PubMed].
  11. Seifert U., Berndl K. and Lipowsky R., Phys. Rev. A 44 (1991) 1182 [CrossRef] [PubMed].
  12. Miao L., et al., Phys. Rev. A 43 (1991) 6843 [CrossRef] [PubMed].
  13. Miao L., Seifert U., Wortis M. and D $\ddot{\textrm{o}}$bereiner H.-G., Phys. Rev. E 49 (1994) 5389 [CrossRef].
  14. Wintz W., D $\ddot{\textrm{o}}$bereiner H.-G. and Seifert U., Europhys. Lett. 33 (1996) 403 [EDP Sciences] [CrossRef].
  15. Mutz M. and Bensimon D., Phys. Rev. A 43 (1991) 4525 [CrossRef] [PubMed].
  16. Fourcade B., Mutz M. and Bensimon D., Phys. Rev. Lett. 68 (1992) 2551 [CrossRef] [PubMed].
  17. Michalet X. and Bensimon D., J. Phys. Ii France 5 (1995) 263 [EDP Sciences] [CrossRef].
  18. Michalet X., Bensimon D. and Fourcade B., Phys. Rev. Lett. 72 (1994) 168 [CrossRef] [PubMed].
  19. Michalet X. and Bensimon D., Science 269 (1995) 666 [CrossRef] [PubMed].
  20. Willmore T., Total curvature in Riemannian geometry (Ellis Horwood, Chicester, 1982).
  21. Duplantier B., Physica A 168 (1990) 179 [MathSciNet].
  22. Duplantier B., Goldstein R., Romero-Rochin V. and Pesci A., Phys. Rev. Lett. 65 (1990) 508 [CrossRef] [PubMed].
  23. Seifert U., Phys. Rev. Lett. 66 (1991) 2404 [CrossRef] [PubMed].
  24. Seifert U., J. Phys. A: Math. Gen. 24 (1991) L573 [CrossRef].
  25. Fourcade B., J. Phys. Ii France 2 (1992) 1705 [EDP Sciences] [CrossRef].
  26. Julicher F., Seifert U. and Lipowsky R., J. Phys. Ii France 3 (1993) 1681 [EDP Sciences] [CrossRef].
  27. Julicher F., Seifert U. and Lipowsky R., Phys. Rev. Lett. 71 (1993) 452 [CrossRef] [PubMed].
  28. Pinkall U. and Sterling I., Math. Intelligencer 9 (1987) 38.
  29. Hsu L., Kusner R. and Sullivan J., Experimental Math. 1 (1992) 191 [MathSciNet].
  30. Kusner R., Pacific J. Math. 138 (1989) 317 [MathSciNet].
  31. Thomsen G., Abh. Math. Sem. Univ. Hamburg 3 (1923) 31.
  32. Blaschke W., Vorlesungen $\ddot{\textrm{u}}$ber Differentialgeometrie (Springer, Berlin, 1929).
  33. Lawson H., Ann. Math. 92 (1970) 335 [MathSciNet].
  34. Karcher H., Pinkall U. and Sterling I., J. Differential Geometry 28 (1988) 169 [MathSciNet].
  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 topological 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 $\vert a\vert \leftarrow \infty$ 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 [CrossRef] [EDP Sciences].
  42. Evans E. and Needham D., J. Phys. Chem. 91 (1987) 4219 [CrossRef].
  43. Duwe H., Kus J. and Sackmann E., J. Phys. France 51 (1990) 945 [CrossRef] [EDP Sciences].
  44. Mutz M. and Helfrich W., J. Phys. France 51 (1990) 991 [CrossRef] [EDP Sciences].
  45. All known surfaces which are solutions of curvature models for vesicle shapes have at least two mirror planes and obey equation (31) by symmetry. In principle, C2h-symmetry would be sufficient to satisfy equation (31) ( C2h-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. Equation (C.4) shows that any surface which obey $\tilde{\textrm{H}}^{2}+1+4\delta\tilde{\textrm{H}}/\delta\tilde{\epsilon}$= 0, is also a stationary solution of the Willmore functional with $\delta G = 0.$ However, no surface with $\delta G = 0$ is known which does not correspond to a minimal surface [28].
  49. Spivak M., Differential Geometry (Publish or Perish, Houston, 1979).