## 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

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

*bending*content and a class of deformations that leave it unchanged. These are the*bending-neutral*deformations, fullycharacterized 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