A Ginzburg-Landau model with topologically induced free discontinuities

In this talk I would like to present a joint work with B. Merlet and V. Millot about a variational model for defects in the ripple phase of lipid bilayers. The model is of Ginzburg-Landau type with an additional jump term. This adds a Mumford-Shah flavor to the problem. We will show that the limiting problem contains both points and line singularities. The limiting energy sees competition between the classical renormalized energy of the vortex points and a term reminiscent of the Steiner problem connecting these points. If time permits, I will also show how the regularity results obtained for the limiting problem can be lifted to the minimizers of the original one.