  Motivated by experiments and formal asymptotic expansions in the physics
literature, Maor and Shachar (J. Elasticity 134 (2019), 149-173) studied the
behaviour of a model elastic energy of maps between manifolds with incompatible
metrics. For thin objects they analysed the scaling of the minimal elastic
energy as a function of the thickness. In particular they showed that for maps
from a ball of radius h in an oriented Riemannian manifold to Euclidean space,
the infimum of a model elastic energy per unit volume scales like the fourth
power of h and after rescaling one gets convergence to a quadratic expression
in the curvature tensor R(p), where p denotes the centre of the ball. In this
paper we show the same result for general compact oriented Riemannian targets
with R(p) replaced by a suitable difference of the curvature tensors in the
target and the domain, thus answering Open Question 1 in the paper by Maor and
Shachar. The result extends noncompact targets provided they satisfy a uniform
regularity condition. A key idea in the proof is to use Lipschitz
approximations to define a suitable notion of convergence.
