Nonuniqueness for Willmore surfaces of revolution satisfying Dirichlet boundary data

DOI10.1007/s12220-015-9639-xzbMath1353.53065OpenAlexW1653618295MaRDI QIDQ345274

Sascha Eichmann

Publication date: 1 December 2016

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

Full work available at URL: https://doi.org/10.1007/s12220-015-9639-x

zbMATH Keywords

Dirichlet boundary conditionsWillmore surfacesurface of revolutionBernstein-type theoremelastic curvesnonuniqueness

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Boundary values of solutions to elliptic equations and elliptic systems (35J67) 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 (9)

Connected surfaces with boundary minimizing the Willmore energy ⋮ Stationary surfaces with boundaries ⋮ Willmore Obstacle Problems under Dirichlet Boundary Conditions ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ On the convergence of the elastic flow in the hyperbolic plane ⋮ Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution ⋮ Symmetry for Willmore surfaces of revolution ⋮ 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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