  The three-dimensional shapes of thin lamina such as leaves, flowers,
feathers, wings etc, are driven by the differential strain induced by the
relative growth. The growth takes place through variations in the Riemannian
metric, given on the thin sheet as a function of location in the central plane
and also across its thickness. The shape is then a consequence of elastic
energy minimization on the frustrated geometrical object. Here we provide a
rigorous derivation of the asymptotic theories for shapes of residually
strained thin lamina with nontrivial curvatures, i.e. growing elastic shells in
both the weakly and strongly curved regimes, generalizing earlier results for
the growth of nominally flat plates. The different theories are distinguished
by the scaling of the mid-surface curvature relative to the inverse thickness
and growth strain, and also allow us to generalize the classical F\"oppl-von
K\'arm\'an energy to theories of prestrained shallow shells.
