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2007-48

Rotationally symmetric classical solutions to the Dirichlet problem for Willmore surfaces

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


Series: 2007-48, Preprints

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

Abstract:
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

Keywords:
rotationally symmetric Willmore surfaces, hyperbolic half plane

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