Crystals and liquid crystals confined to curved geometries

This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the interaction of defects with the underlying curvature. This chapter concludes with two cases of three-dimensional nematic phases confined to spaces with curved boundaries, namely a torus and a spherical shell.