In my talk, I will present a theoretical, numerical and experimental study of a novel elastic body – the non-Euclidean minimal spring. This spring is a ribbon with a hyperbolic reference metric, that can be embedded as a minimal surface. Two of these minimal embeddings are the catenoid and the helicoid which have the minimal and maximal pitch among all the minimal embeddings, respectivly.  I will show that the existence of a continuous isometric transformation from a cathenoid to a helicoid, which involves only minimal surfaces, leads to a complete degeneracy of the bulk elastic energy of this object under extension.
This degeneracy is removed only by boundary layer effects. As a result, the mechanical properties of the minimal spring are unusual: the spring is ultra-soft, linear to a high degree and its rigidity does not depend on its width. A numerical study confirms these predictions.
Finally, I will present the first experimental realization of minimal springs, using a novel system for the “lithography of curvature” on hydrogel sheets.