  In this contribution to the proceedings of the 11th Mathematical Society of
Japan (MSJ) Seasonal Institute (July 2018) we give an overview of some recent
work on a mathematical model for small deformations of a spherical membrane.
The idea is to consider perturbations to minimisers of a surface geometric
energy. The model is obtained from consideration of second order approximations
to a perturbed energy. In particular, the considered problems involve particle
constraints and surface phase field energies.
