View AbstractAbstract: Non-Euclidean, or incompatible elasticity is an elastic theory for bodies that do not have a reference, stress-free configuration. It applies to many systems, in which the elastic body undergoes inhomogeneous growth (e.g. plants, self-assembled molecules). Mathematically, it is a geometric calculus of variations question of finding the "most isometric" immersion of a Riemannian manifold (M,g) into Euclidean space of the same dimension.
Much of the research in non-Euclidean elasticity is concerned with elastic bodies that have one or more slender dimensions (such as leaves), and finding appropriate dimensionally-reduced models for them.
In this talk I will give an introduction to non-Euclidean elasticity, and then focus on thin bodies and present some recent results on the relations between their elastic behavior and their curvature.
Based on joint work with Asaf Shachar.