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Asymptotic behaviour for Willmore surfaces of revolution under natural boundary conditions

by S. Jachalski.

Series: 2010-09, Preprints

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

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