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arXiv · 2107.12500

The Euler-Helfrich Functional

Bennett Palmer·Alvaro Pampano
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Abstract

We investigate equilibrium configurations for surface energies which contain the squared $L^2$ norm of the difference of the mean curvature H and the spontaneous curvature $c_o$ 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.

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Bennett Palmer, Alvaro Pampano. 2021-07-26. The Euler-Helfrich Functional. https://arxiv.org/abs/2107.12500

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