Journal
JOURNAL OF GEOMETRIC ANALYSIS
Volume 27, Issue 1, Pages 618-642Publisher
SPRINGER
DOI: 10.1007/s12220-016-9692-0
Keywords
Dirichlet boundary conditions; Symmetry; Willmore surfaces of revolution
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We will show a symmetry result concerning Willmore surfaces of revolution which satisfy symmetric Dirichlet data. The first step is to find a regular energy minimizing surface. We will do this by carefully modifying a minimizing sequence using an idea by Dall'Acqua, Deckelnick & Grunau. After this we will establish a priori estimates for non-symmetric solutions, in which an order-reduction argument by Langer & Singer will be essential.
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