Abstract
We consider bending theories for thin elastic films obtained by endowing a bounded domain S⊂R2 with a Riemannian metric g. The associated elastic energy is given by a nonlinear isometry-constrained bending energy functional, which is a natural generalisation of Kirchhoff's plate functional to metrics with possibly nonzero Gauss curvature. We introduce and discuss a natural notion of stationarity for such functionals.We then show that all rotationally symmetric immersions of the unit disk are stationary in that sense, and we give examples of smooth metrics g leading to functionals with infinitely many stationary points. Finally, we implement our general approach in the case when g has positive Gauss curvature.
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