Nonlinear bending theories for non Euclidean plates

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Thin growing tissues (such as plant leaves) can be modelled by a bounded domain S⊂ R² endowed with a Riemannian metric g, which models the internal strains caused by the differential growth of the tissue. The elastic energy is given by a nonlinear isometry-constrained bending energy functional which is a natural generalization of Kirchhoff's plate functional. We introduce and discuss a natural notion of (possibly non-minimising) stationarity points. We show that rotationally symmetric immersions of the unit disk are stationary, and we give examples of metrics g leading to functionals with infinitely many stationary points.