A strict inequality for the minimization of the Willmore functional under isoperimetric constraint

DOI10.1515/acv-2021-0002zbMath1520.49020arXiv2011.14904OpenAlexW3108891874MaRDI QIDQ6165629

Christian Scharrer, Andrea Mondino

Publication date: 6 July 2023

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.14904

zbMATH Keywords

Willmore functionalexistence of minimizersisoperimetric constraintstrict energy inequality

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05)

Related Items (3)

Li-Yau inequalities for the Helfrich functional and applications ⋮ The Willmore flow with prescribed isoperimetric ratio ⋮ Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs

Cites Work

• \(W^{2,2}\)-conformal immersions of a closed Riemann surface into \(\mathbb{R}^n\)
• A characteristic property of spheres
• Comparison surfaces for the Willmore problem
• Existence of surfaces minimizing the Willmore functional
• On surfaces of finite total curvature
• Existence and regularity of spheres minimising the Canham-Helfrich energy
• Willmore minimizers with prescribed isoperimetric ratio
• Min-max theory and the Willmore conjecture
• Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint
• Complete minimal surfaces in \(S^ 3\)
• The large genus limit of the infimum of the Willmore energy
• The volume preserving mean curvature flow.
• ON TOTAL MEAN CURVATURES
• Asymptotics of Willmore Minimizers with Prescribed Small Isoperimetric Ratio
• Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms
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