Neutral Deformation Modes of Minimal Surfaces

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.