Bending-Neutral Deformations of Minimal Surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909283919069184 |
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| author | Sonnet, André M. Virga, Epifanio G. |
| author_facet | Sonnet, André M. Virga, Epifanio G. |
| contents | Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we identify a bending content and a class of deformations that leave it unchanged. These are the bending-neutral deformations, fully characterized by an integrability condition; they preserve normals. We prove that (1) every minimal surface is transformed into a minimal surface by a bending-neutral deformation, (2) given two minimal surfaces with the same system of normals, there is a bending-neutral deformation that maps one into the other, and (3) all minimal surfaces have indeed a universal bending content. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16169 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bending-Neutral Deformations of Minimal Surfaces Sonnet, André M. Virga, Epifanio G. Differential Geometry Mathematical Physics Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we identify a bending content and a class of deformations that leave it unchanged. These are the bending-neutral deformations, fully characterized by an integrability condition; they preserve normals. We prove that (1) every minimal surface is transformed into a minimal surface by a bending-neutral deformation, (2) given two minimal surfaces with the same system of normals, there is a bending-neutral deformation that maps one into the other, and (3) all minimal surfaces have indeed a universal bending content. |
| title | Bending-Neutral Deformations of Minimal Surfaces |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2405.16169 |