Bending-neutral deformations of minimal surfaces
Sonnet, André M. and Virga, Epifanio G. (2024) Bending-neutral deformations of minimal surfaces. Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences. ISSN 1471-2962 (In Press) (https://doi.org/10.1098/rspa.2024.0394)
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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.
ORCID iDs
Sonnet, André M.![ORCID logo](/images/orcid_16x16.png)
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Item type: Article ID code: 90368 Dates: DateEvent23 August 2024Published23 August 2024Accepted25 May 2024SubmittedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 27 Aug 2024 10:08 Last modified: 29 Aug 2024 14:38 URI: https://strathprints.strath.ac.uk/id/eprint/90368