An Analysis on the Shape Equation for Biconcave Axisymmetric Vesicles

2000/01/19 by Thomas Kwok-keung Au, Au, Thomas Kwok-keung, Tom Yau-heng Wan +1
Biochemistry, Genetics and Molecular Biology · Chemistry · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Force Microscopy Techniques and Applications #Lipid Membrane Structure and Behavior #Surfactants and Colloidal Systems #math.AP

paper · pdf · doi:10.48550/arxiv.math/0001103

23 pages, 1 figure, AMSLaTeX, major revision of "On the existence of biconcave shape vesicles". No offset problem

openalex publication_date 2000/01/19 · arxiv created 2001/02/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variation equation is analyzed in detail. This leads to simple conditions which guarantee the solution the information about the geometry.

Citations

• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces

Related

• Conditions for the Formation of Axisymmetric Biconcave Vesicles
• Physical Parameters for Biconcave Shape Vesicles
• A series representation of the nonlinear equation for axisymmetrical fluid membrane shape
• Local sensitivity analysis of the `Membrane shape equation' derived from the Helfrich energy
• Stationary shapes of axisymmetric vesicles beyond lowest-energy configurations