English

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 L2L^2 norm of the difference of the mean curvature H and the spontaneous curvature coc_o 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.

Keywords

Cite

@article{arxiv.2107.12500,
  title  = {The Euler-Helfrich Functional},
  author = {Bennett Palmer and Alvaro Pampano},
  journal= {arXiv preprint arXiv:2107.12500},
  year   = {2021}
}
R2 v1 2026-06-24T04:32:43.290Z