On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves

DOI10.1051/cocv/2020049zbMath1467.49041arXiv1810.07662OpenAlexW3044774149MaRDI QIDQ4999579

Marco Pozzetta

Publication date: 7 July 2021

Published in: ESAIM: Control, Optimisation and Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.07662

zbMATH Keywords

existenceimmersed surfacesWillmore energyNavier boundary conditionsSimon's ambient approachWillmore surfaces with boundary

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Surfaces in Euclidean and related spaces (53A05)

Related Items (4)

Stationary surfaces with boundaries ⋮ Willmore Obstacle Problems under Dirichlet Boundary Conditions ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local solutions to a free boundary problem for the Willmore functional
• Nonuniqueness for Willmore surfaces of revolution satisfying Dirichlet boundary data
• Unstable Willmore surfaces of revolution subject to natural boundary conditions
• Variational principles for immersed surfaces with \(L^2\)-bounded second fundamental form
• Symmetric Willmore surfaces of revolution satisfying natural boundary conditions
• \(n\)-harmonic coordinates and the regularity of conformal mappings
• Analysis aspects of Willmore surfaces
• A compactness theorem for surfaces with \(L_ p\)-bounded second fundamental form
• Curvature varifolds with boundary
• The Helfrich boundary value problem
• Uniqueness for the homogeneous Dirichlet Willmore boundary value problem
• Removability of point singularities of Willmore surfaces
• Existence of surfaces minimizing the Willmore functional
• Willmore surfaces of revolution with two prescribed boundary circles
• Existence and regularity of spheres minimising the Canham-Helfrich energy
• A resolution of the Poisson problem for elastic plates
• Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution
• Connected surfaces with boundary minimizing the Willmore energy
• Willmore minimizers with prescribed isoperimetric ratio
• Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions
• Minimising a relaxed Willmore functional for graphs subject to boundary conditions
• The Willmore boundary problem
• 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
• Global Analysis of Minimal Surfaces
• A Navier boundary value problem for Willmore surfaces of revolution
• Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms
• Classical solutions to the Dirichlet problem for Willmore surfaces of revolution

This page was built for publication: On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves