Uniqueness theorems for Willmore surfaces with fixed and free boundaries

DOI10.1512/IUMJ.2000.49.1872zbMath0991.53002OpenAlexW2091396588MaRDI QIDQ2733839

Bennett Palmer

Publication date: 12 August 2001

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2000.49.1872

zbMATH Keywords

free boundary problemvariational problemsWillmore surfaceWillmore discs

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Variational problems in infinite-dimensional spaces (58E99)

Related Items (13)

Local solutions to a free boundary problem for the Willmore functional ⋮ Noether's theorem and the Willmore functional ⋮ Stationary surfaces with boundaries ⋮ Unstable Willmore surfaces of revolution subject to natural boundary conditions ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ Sufficient conditions for Willmore immersions in \(\mathbb R^3\) to be minimal surfaces ⋮ Uniqueness for the homogeneous Dirichlet Willmore boundary value problem ⋮ Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary ⋮ Minimizing configurations for elastic surface energies with elastic boundaries ⋮ On time-like Willmore surfaces in Minkowski space ⋮ Regarding the Euler-Plateau problem with elastic modulus ⋮ On the Plateau–Douglas problem for the Willmore energy of surfaces with planar boundary curves ⋮ The Euler-Helfrich functional

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