https://doi.org/10.1140/epjb/e2002-00310-y
New solutions of the shape equation
Institute of Biophysics, Bulgarian Academy of Sciences,
Acad. G. Bonchev Str., Bl. 21, 1113 Sofia, Bulgaria
Corresponding author: a mladenov@obzor.bio21.bas.bg
Received:
2
February
2002
Revised:
4
February
2002
Published online:
2
October
2002
The general shape equation describing the forms of vesicles is a highly nonlinear partial differential equation for which only a few explicit solutions are known. These solvable cases are briefly reviewed and a new analytical solution which represents the class of the constant mean curvature surfaces is described. Pearling states of the tubular fluid membranes can be explained as a continuous deformation preserving membrane mean curvature.
PACS: 87.16.Dg – Membranes, bilayers, and vesicles / 68.15.+e – Liquid thin films / 87.10.+e – General theory and mathematical aspects / 02.40.Hw – Classical differential geometry
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
