Small deformations of spherical biomembranes
Charles M. Elliott, Luke Hatcher, Philip J. Herbert
TL;DR
This paper reviews recent mathematical models describing small deformations of spherical biomembranes, focusing on perturbations to energy minimizers and including particle constraints and phase field energies.
Contribution
It introduces a second order approximation framework for analyzing small membrane deformations considering various constraints.
Findings
Developed a mathematical model for small deformations
Analyzed perturbations around energy minimizers
Incorporated particle constraints and phase field energies
Abstract
In this contribution to the proceedings of the 11th Mathematical Society of Japan (MSJ) Seasonal Institute (July 2018) we give an overview of some recent work on a mathematical model for small deformations of a spherical membrane. The idea is to consider perturbations to minimisers of a surface geometric energy. The model is obtained from consideration of second order approximations to a perturbed energy. In particular, the considered problems involve particle constraints and surface phase field energies.
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