  The balance between stretching and bending deformations characterizes shape
transitions of thin elastic sheets. While stretching dominates the mechanical
response in tension, bending dominates in compression after an abrupt buckling
transition. Recently, experimental results in suspended living epithelial
monolayers have shown that, due to the asymmetry in surface stresses generated
by molecular motors across the thickness $e$ of the epithelium, the free edges
of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane
as a result. This suggests that a competition between bending and stretching
sets the morphology of the tissue margin. In this study, we use the framework
of non-euclidean plates to incorporate active pre-strain and spontaneous
curvature to the theory of thin elastic shells. We show that, when the
spontaneous curvature of the sheet scales like $1/e$, stretching and bending
energies have the same scaling in the limit of a vanishingly small thickness
and therefore both compete, in a way that is continuously altered by an
external tension, to define the three-dimensional shape of the tissue.
