Symmetry for Willmore Surfaces of Revolution

We will show a symmetry result concerning Willmore surfaces of revolution which satisfy symmetric Dirichlet data. The first step is to find a regular energy minimizing surface. We will do this by carefully modifying a minimizing sequence using an idea by Dall'Acqua, Deckelnick & Grunau. After this we will establish a priori estimates for non-symmetric solutions, in which an order-reduction argument by Langer & Singer will be essential.