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

Small deformations of spherical biomembranes