Neutral deformation modes of minimal surfaces

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Sonnet, André M. and Virga, Epifanio G. (2026) Neutral deformation modes of minimal surfaces. Journal of Elasticity, 158 (2). 25. ISSN 0374-3535 (https://doi.org/10.1007/s10659-026-10201-8)

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Abstract

Stretching, drilling, and bending are the independent deformation modes of a thin shell, each of which has an individual energy content. When the energy content of a mode vanishes, that mode is neutral. We characterize all neutral modes of deformation of minimal surfaces into minimal surfaces. A hierarchy is found among these: a stretching neutral mode (which is an isometry) is also drilling neutral, and a drilling neutral mode is also bending neutral. Thus, all isometries of a minimal surface are globally neutral and give rise to soft elasticity. More generally, all minimal surfaces can be classified relative to a reference one in terms of three energy contents, which can be given in closed form.

ORCID iDs

Sonnet, André M. ORCID logoORCID: https://orcid.org/0000-0003-2583-7897 and Virga, Epifanio G.;
CORE (COnnecting REpositories)