Minimizers of the Willmore functional with a small area constraint
  We show the existence of a smooth spherical surface minimizing the Willmore functional subject to an area constraint in a compact Riemannian three-manifold, provided the area is small enough. Moreover, we classify complete surfaces of Willmore type with positive mean curvature in Riemannian three-manifolds. 
Tobias Lamm and Jan Metzger
math.DG math.AP