Open Access
2014 Cylindrical Shapes of Helfrich Spontaneous-Curvature Model
Vladimir I. Pulov, Eddie J. Chakarov
J. Geom. Symmetry Phys. 36: 99-115 (2014). DOI: 10.7546/jgsp-36-2014-99-115


The governing equation of the Helfrich spontaneous-curvature model is the Helfrich equation. It is a coordinate free equation that describes the equilibrium shapes of biological (fluid) membranes. We make use of the conformal metric representation of the Helfrich equation and by applying the symmetry group reduction method we obtain a translationally invariant solution. Based on that solution, we derive analytic expressions for the position vector of special cylindrical equilibrium shapes. Plots of the graphs of some closed directrices of these shapes are presented.


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Vladimir I. Pulov. Eddie J. Chakarov. "Cylindrical Shapes of Helfrich Spontaneous-Curvature Model." J. Geom. Symmetry Phys. 36 99 - 115, 2014.


Published: 2014
First available in Project Euclid: 27 May 2017

zbMATH: 1326.74081
MathSciNet: MR3379443
Digital Object Identifier: 10.7546/jgsp-36-2014-99-115

Rights: Copyright © 2014 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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