Symmetry for Willmore surfaces of revolution

DOI10.1007/s12220-016-9692-0zbMath1364.34027OpenAlexW2293290206MaRDI QIDQ522490

Sascha Eichmann, Amos N. Koeller

Publication date: 13 April 2017

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-016-9692-0

zbMATH Keywords

symmetryDirichlet boundary conditionsWillmore surfaces of revolution

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Symmetries, invariants of ordinary differential equations (34C14) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)

Related Items

Willmore Obstacle Problems under Dirichlet Boundary Conditions ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ A resolution of the Poisson problem for elastic plates ⋮ Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution ⋮ Elastic curves and phase transitions ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ Existence and uniqueness for variational problem from progressive Lens design ⋮ Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions

Cites Work

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• Nonuniqueness for Willmore surfaces of revolution satisfying Dirichlet boundary data
• Symmetric Willmore surfaces of revolution satisfying natural boundary conditions
• The total squared curvature of closed curves
• Willmore surfaces of revolution with two prescribed boundary circles
• The Willmore boundary problem
• Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
• Boundary value problems for variational integrals involving surface curvatures
• Curves in the Hyperbolic Plane and mean Curvature of Tori in 3-Space
• [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

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