Stability of Membranes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866909067869421568 |
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| author | Palmer, Bennett Pampano, Alvaro |
| author_facet | Palmer, Bennett Pampano, Alvaro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05285 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of Membranes Palmer, Bennett Pampano, Alvaro Differential Geometry 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. |
| title | Stability of Membranes |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2401.05285 |