Reflection of Willmore Surfaces with Free Boundaries

DOI10.4153/S0008414X20000164zbMath1482.49049arXiv1906.05720MaRDI QIDQ4999642

Tobias Lamm, Ernst Christoph Kuwert

Publication date: 7 July 2021

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.05720

zbMATH Keywords

free boundary problemWillmore surfaces

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Optimization of shapes other than minimal surfaces (49Q10)

Cites Work

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• Local solutions to a free boundary problem for the Willmore functional
• \(W^{2,2}\)-conformal immersions of a closed Riemann surface into \(\mathbb{R}^n\)
• A duality theorem for Willmore surfaces
• Analysis aspects of Willmore surfaces
• Removability of point singularities of Willmore surfaces
• Gradient flow for the Willmore functional
• Existence of surfaces minimizing the Willmore functional
• A resolution of the Poisson problem for elastic plates
• Branched Willmore spheres
• The Willmore boundary problem
• A Viscosity method for the min-max construction of closed geodesics
• Boundary value problems for variational integrals involving surface curvatures
• A Navier boundary value problem for Willmore surfaces of revolution
• Conformal geometry and complete minimal surfaces

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