Unstable Willmore surfaces of revolution subject to natural boundary conditions

DOI10.1007/s00526-012-0551-yzbMath1280.35061OpenAlexW2086099083MaRDI QIDQ376600

Glen Wheeler, Anna Dall'Acqua, Klaus Deckelnick

Publication date: 5 November 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://ro.uow.edu.au/cgi/viewcontent.cgi?article=3072&context=eispapers

zbMATH Keywords

Willmore functionalsymmetric surfaces of revolutionunstable critical points

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Methods involving semicontinuity and convergence; relaxation (49J45) Optimization of shapes other than minimal surfaces (49Q10) Variational problems in infinite-dimensional spaces (58E99) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Quasilinear elliptic equations with mean curvature operator (35J93)

Related Items

Connected surfaces with boundary minimizing the Willmore energy ⋮ Noether's theorem and the Willmore functional ⋮ Stationary surfaces with boundaries ⋮ A classification theorem for Helfrich surfaces ⋮ On the convergence of the Willmore flow with 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 ⋮ Boundary value problems for Willmore curves in \(\mathbb {R}^2\) ⋮ Willmore Surfaces in Three-Dimensional Simply Isotropic Spaces $$\mathbb {I}_3^1$$ ⋮ Elastic curves and phase transitions ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions ⋮ On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves

Cites Work

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• Local Palais-Smale sequences for the Willmore functional
• Symmetric Willmore surfaces of revolution satisfying natural boundary conditions
• A duality theorem for Willmore surfaces
• Analysis aspects of Willmore surfaces
• The conformal Gauss map and the stability of Willmore surfaces
• Existence of surfaces minimizing the Willmore functional
• Willmore surfaces of revolution with two prescribed boundary circles
• Curve straightening and a minimax argument for closed elastic curves
• The Willmore boundary problem
• The clamped-plate equation for the Limac con
• Uniqueness theorems for Willmore surfaces with fixed and free boundaries
• Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
• Boundary value problems for variational integrals involving surface curvatures
• The Asymptotic Shape of a Boundary Layer of Symmetric Willmore Surfaces of Revolution
• 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]
• Ein Beweis der Willmoreschen Vermutung für Kanaltori.
• Closed surfaces with bounds on their Willmore energy
• Classical solutions to the Dirichlet problem for Willmore surfaces of revolution

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