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2010-09

Asymptotic behaviour for Willmore surfaces of revolution under natural boundary conditions

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