Foliation of asymptotically flat manifolds by surfaces of Willmore type

In this talk I will present aspects of the construction of Willmore type surfaces in asymptotically flat manifolds. The surfaces in question are critical points of the Willmore functional subject to an area constraint. The position vector of these surfaces satisfies a quasi-linear elliptic equation of fourth order. The main result ist that under suitable asymptotic conditions the asymptotic end of an asymptotically flat 3-manifold is foliated by surfaces of Willmore type that converge to Euclidean spheres as the area becomes large.