Kirchhoff's nonlinear bending theory of plates

Kirchhoff's nonlinear plate theory arises as a thin film asymptotic limit from three dimensional elasticity. It lives on intrinsically flat surfaces, i.e., on deformations of two dimensional films into three dimensional euclidean space which do not stretch the film. In the first part of the talk I will explain the local and global structure enjoyed by such 'non-stretching' deformations.

The energy functional corresponding to Kirchhoff's plate theory agrees with a constrained version of the Willmore functional from differential geometry. In the second part of the talk I will recall some facts about the Willmore functional and I will discuss minimizers of Kirchhoff's plate functional.