Bending-neutral deformations of minimal surfaces

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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, 480 (2300). 20240394. ISSN 1471-2962 (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; they preserve normals. We prove that: (i) every minimal surface is transformed into a minimal surface by a bending-neutral deformation; (ii) given two minimal surfaces with the same system of normals, there is a bending-neutral deformation that maps one into the other; and (iii) all minimal surfaces have indeed a universal bending content.

ORCID iDs

Sonnet, André M. ORCID logoORCID: https://orcid.org/0000-0003-2583-7897 and Virga, Epifanio G.;
  • Item type:Article
    ID code:90368
    Dates:
    Date
    Event
    30 October 2024
    Published
    23 August 2024
    Accepted
    25 May 2024
    Submitted
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:27 Aug 2024 10:08
    Last modified:18 Nov 2024 08:56
    URI:https://strathprints.strath.ac.uk/id/eprint/90368
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