Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
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Publication:3074547
DOI10.1515/ACV.2010.022zbMath1213.49050OpenAlexW1987601019MaRDI QIDQ3074547
Hans-Christoph Grunau, Friedhelm Schieweck, Anna Dall'Acqua, Steffen Fröhlich
Publication date: 9 February 2011
Published in: Advances in Calculus of Variations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1515/acv.2010.022
Nonlinear boundary value problems for linear elliptic equations (35J65) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10) Nonlinear ordinary differential operators (34L30)
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Cites Work
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- Analysis aspects of Willmore surfaces
- Willmore tori in the 4-sphere with nontrivial normal bundle
- A level set formulation for Willmore flow
- The Willmore boundary problem
- Error analysis of a finite element method for the Willmore flow of graphs
- Boundary value problems for the one-dimensional Willmore equation
- Curves in the Hyperbolic Plane and mean Curvature of Tori in 3-Space
- Stability and Symmetry in the Navier Problem for the One-Dimensional Willmore Equation
- A Navier boundary value problem for Willmore surfaces of revolution
- [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
- Classical solutions to the Dirichlet problem for Willmore surfaces of revolution
- On rigid string instantons in four dimensions
