by S. Jachalski.

**Series:** 2010-09, Preprints

- MSC:
- 49Q10 Optimization of shapes other than minimal surfaces
- 53C42 Immersions (minimal, prescribed curvature, tight, etc.)
- 35J65 Nonlinear boundary value problems for linear elliptic equations
- 34L30 Nonlinear ordinary differential operators

**Abstract:**

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.

**Keywords:**

Willmore surface of revolution, natural boundary conditions, convergence