Ernst Kuwert

For a surface in Euclidean space, the Willmore energy is given by integrating the squared mean curvature over the surface, and can be viewed intuitively as a bending energy. It is invariant under conformal transformations of space, which is beautiful from the viewpoint of geometry but poses difficulties in the analysis : sequences of surfaces with uniformly bounded energy may degenerate. We eventually present a bi-Lipschitz type estimate which allows to overcome the problem in relevant situations.