Date:

Wed, 12/05/202112:00-13:00

__: Asymptotic rigidity for shells in non-Euclidean elasticity__

**Title**__: An elastic shell can be modeled as a 2-dimensional Riemannian manifold__

**Abstract***(M,g)* endowed with a "reference second fundamental form"

*b*.

The elastic energy

*E(f)* of an embedding

*f: (M,g) → ℝ* then measures the deviation of the first and second fundamental forms of the embedded surface from the reference ones.

^{3}A classical result asserts that if g and b satisfy some compatibility conditions — the Gauss–Codazzi equations — then there exists a configuration f with zero elastic energy.

However, it is not clear that

*E* attains its minimum. It is therefore natural to ask whether

*inf E = 0*implies that

*g*and

*b*are compatible, and in this case, whether any minimizing sequence converges to a zero-energy configuration.

In this lecture I will show that this is indeed true, as well as generalizations of this result. I will present a sketch of the proof of this theorem, emphasizing its main ideas.

Based on a joint work with Raz Kupferman and Cy Maor.