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arXiv · 2401.05285

Stability of Membranes

Bennett Palmer·Alvaro Pampano
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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.

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Bennett Palmer, Alvaro Pampano. 2024-01-10. Stability of Membranes. https://arxiv.org/abs/2401.05285

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