For any two-dimensional surface   f : Σ → R², the Willmore functional is given by ¼∫ _Σ H² dμ , where H is the mean curvature and μ is the area measure. The central geometric feature of the functional is its invariance under the Möbius group of Rⁿ. The corresponding Euler Lagrange equation is a fourth order quasilinear elliptic system, whose solutions are called Willmore surfaces.

The lecture starts with classical material on the geometry of the functional, including basic formulae and inequalities due to Willmore and Li-Yau. The main focus will then be on analytic questions which have been addressed in joint work with Reiner Schätzle (Universität Tübingen) in the last years. Specifically, we plan to discuss the Willmore flow, the removability of point singularities in codimension one Willmore surfaces and, if times permits, a recent bilipschitz estimate for surfaces of low Willmore energy.

The course requires no prerequisites. At a later point, we will need one or two results from the literature which will be stated without proof.

Zeit:       Mittwoch, 14:15-16
Ort:        HG G 43 (Hermann-Weyl-Zimmer)
Beginn:   3. Oktober
 

M. Struwe