Stability of Membranes
Differential Geometry
2024-01-11 v1
Abstract
In [12], the authors studied a particular class of equilibrium solutions of the Helfrich energy which satisfy a second order condition called the reduced membrane equation. In this paper we develop and apply a second variation formula for the Helfrich energy for this class of surfaces. The reduced membrane equation also arises as the Euler-Lagrange equation for the area of surfaces under the action of gravity in the three dimensional hyperbolic space. We study the second variation of this functional for a particular example.
Cite
@article{arxiv.2401.05285,
title = {Stability of Membranes},
author = {Bennett Palmer and Alvaro Pampano},
journal= {arXiv preprint arXiv:2401.05285},
year = {2024}
}