by S. Jachalski.
Series: 2010-09, Preprints
We consider the Willmore boundary value problem for surfaces of revolution where the position at the boundary is fixed, while a condition on the curvature arises as natural boundary condition. We study the limit when the radii of the boundary circles converge to $0$, while the ``length'' of the surfaces of revolution is kept fixed. This singular limit is shown to be the sphere.
Willmore surface of revolution, natural boundary conditions, convergence