10-09
Asymptotic behaviour for Willmore surfaces of revolution under natural boundary conditions
by S. Jachalski
Preprint series: 10-09, Preprints
- MSC:
- 49Q10 Optimization of the shape other than minimal surfaces, See also {73K40, 90C90}
- 53C42 Immersions (minimal, prescribed curvature, tight, etc.), See also {49Q05, 49Q10, 53A10, 57R40, 57R42}
- 35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
- 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
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