Neutral Deformation Modes of Minimal Surfaces
Differential Geometry
2025-10-16 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2510.12987,
title = {Neutral Deformation Modes of Minimal Surfaces},
author = {Ande M. Sonnet and Epifanio G. Virga},
journal= {arXiv preprint arXiv:2510.12987},
year = {2025}
}