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Rotationally symmetric classical solutions to the Dirichlet problem for Willmore surfaces

by Dall'Acqua, A., Deckelnick, K., Grunau, H.-Ch..

Series: 2007-48, Preprints

53C42 Immersions (minimal, prescribed curvature, tight, etc.)
35J65 Nonlinear boundary value problems for linear elliptic equations
49K20 Problems involving partial differential equations

We consider the Willmore equation with Dirichlet boundary conditions for a surface of revolution
obtained by rotating the graph of a positive smooth even function. We show existence of a regular
solution by minimisation. Instead of minimising the Willmore functional we reformulate the problem
in the hyperbolic half plane and we minimise the corresponding

rotationally symmetric Willmore surfaces, hyperbolic half plane

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