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VOL. 8 | 2007 On the Translationally-Invariant Solutions of the Membrane Shape Equation
Vassil M. Vassilev, Peter A. Djondjorov, Ivaïlo M. Mladenov

Editor(s) Ivaïlo M. Mladenov, Manuel de León

Abstract

The membrane shape equation derived by Helfrich and Ou-Yang describes the equilibrium shapes of biomembranes, built by bilayers of amphiphilic molecules, in terms of the mean and Gaussian curvatures of their middle-surfaces. Here, we present a new class of translationally-invariant solutions to this equation in terms of the elliptic functions which completes the solutions found earlier. In this way, all translationally-invariant solutions to the membrane shape equation are determined. Special attention is paid to those translationally-invariant solutions of the membrane shape equation which determine closed cylindrical (tube-like) surfaces (membrane shapes). Several examples of such surfaces are presented.

Information

Published: 1 January 2007
First available in Project Euclid: 13 July 2015

zbMATH: 1125.53008
MathSciNet: MR2341212

Digital Object Identifier: 10.7546/giq-8-2007-312-321

Rights: Copyright © 2007 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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