Geometric structures arising from a variational model for crystal surfaces

Roger Moser, University of Bath. Part of geometry seminar series.

The free energy of a crystal surface can be modelled by an anisotropic area functional, but a model proposed by Herring adds a curvature term as well. The sum of the two can be regarded as a singular perturbation problem and an asymptotic analysis then leads to a limiting variational problem. Here the crystal surfaces are represented by (generalised) polyhedra, and the free energy gives rise to a functional depending on the lengths of the edges. We discuss aspects of this asymptotic analysis and some consequences for the geometric structures emerging thereby.