A phase field model for the optimization of the Willmore energy in the class of connected surfaces

Dr. Patrick Dondl (Durham University)

Thursday 17th October, 2013 14:00-15:00 Maths 326


We consider the problem of minimizing the Willmore energy on confined and connected surfaces with prescribed surface area. To this end, we approximate the surface by a level set function u admitting the value +1 on the inside of the surface and -1 on its outside. The confinement of the surface is now simply given by the domain of definition of u.

A diffuse interface approximation for the area functional, as well as for the Willmore energy are well known. We address the main difficulty, namely the topological constraint of connectedness by a nested minimization of two phase fields, the second one being used to identify connected components of the surface. In this article, we provide a proof of Gamma-convergence of our model to the sharp interface limit. This is joint work with Matthias Röger (TU Dortmund) and Luca Mugnai (MPI Leipzig).

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