Abstract
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. We prove that (1) every minimal surface is transformed into a minimal surface by a bending-neutral deformation and (2) given two minimal surfaces, there is a bending-neutral deformation that maps one into the other. Thus all minimal surfaces have indeed a universal bending content.
characterized by an integrability condition. We prove that (1) every minimal surface is transformed into a minimal surface by a bending-neutral deformation and (2) given two minimal surfaces, there is a bending-neutral deformation that maps one into the other. Thus all minimal surfaces have indeed a universal bending content.
| Original language | English |
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| Journal | Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences |
| DOIs | |
| Publication status | Accepted/In press - 23 Aug 2024 |
Keywords
- plates
- shells
- minimal surfaces