Neutral Deformation Modes of Minimal Surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911210999382016 |
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| author | Sonnet, Ande M. Virga, Epifanio G. |
| author_facet | Sonnet, Ande M. Virga, Epifanio G. |
| contents | Stretching, drilling, and bending are the independent deformation modes of a thin shell, each of which has an individual energy content. When the energy content of a mode vanishes, that mode is neutral. We characterize all neutral modes of deformation of minimal surfaces into minimal surfaces. A hierarchy is found among these: a stretching neutral mode (which is an isometry) is also drilling neutral, and a drilling neutral mode is also bending neutral. Thus, all isometries of a minimal surface are globally neutral and give rise to soft elasticity. More generally, all minimal surfaces can be classified relative to a reference one in terms of three energy contents, which can be given in closed form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12987 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neutral Deformation Modes of Minimal Surfaces Sonnet, Ande M. Virga, Epifanio G. Differential Geometry Mathematical Physics Stretching, drilling, and bending are the independent deformation modes of a thin shell, each of which has an individual energy content. When the energy content of a mode vanishes, that mode is neutral. We characterize all neutral modes of deformation of minimal surfaces into minimal surfaces. A hierarchy is found among these: a stretching neutral mode (which is an isometry) is also drilling neutral, and a drilling neutral mode is also bending neutral. Thus, all isometries of a minimal surface are globally neutral and give rise to soft elasticity. More generally, all minimal surfaces can be classified relative to a reference one in terms of three energy contents, which can be given in closed form. |
| title | Neutral Deformation Modes of Minimal Surfaces |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2510.12987 |