The Euler-Helfrich Functional
Differential Geometry
2021-07-28 v1 Analysis of PDEs
Abstract
We investigate equilibrium configurations for surface energies which contain the squared norm of the difference of the mean curvature H and the spontaneous curvature coupled with the elastic energy of the boundary curve, which we studied previously in [23]. It is shown that if a critical surface for this type of functional is axially symmetric, then it satisfies a simpler second order variational problem. Many examples of solutions of this are given.
Cite
@article{arxiv.2107.12500,
title = {The Euler-Helfrich Functional},
author = {Bennett Palmer and Alvaro Pampano},
journal= {arXiv preprint arXiv:2107.12500},
year = {2021}
}