Willmore surfaces of revolution with two prescribed boundary circles

DOI10.1007/S12220-011-9248-2zbMath1257.49044OpenAlexW1965043466MaRDI QIDQ1935482

Matthias Bergner, Anna Dall'Acqua, Steffen Fröhlich

Publication date: 18 February 2013

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

Full work available at URL: https://doi.org/10.1007/s12220-011-9248-2

zbMATH Keywords

Willmore surfacesurface of revolutionnatural boundary conditions

Mathematics Subject Classification ID

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)

Related Items (10)

Connected surfaces with boundary minimizing the Willmore energy ⋮ Nonuniqueness for Willmore surfaces of revolution satisfying Dirichlet boundary data ⋮ Unstable Willmore surfaces of revolution subject to natural boundary conditions ⋮ Sufficient conditions for Willmore immersions in \(\mathbb R^3\) to be minimal surfaces ⋮ 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 ⋮ Symmetry for Willmore surfaces of revolution ⋮ Boundary value problems for Willmore curves in \(\mathbb {R}^2\) ⋮ 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

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