On the Canham problem: bending energy minimizers for any genus and isoperimetric ratio

DOI10.1007/s00205-022-01833-wOpenAlexW3153852084MaRDI QIDQ2682943

Peter McGrath, Robert B. Kusner

Publication date: 1 February 2023

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.10045

zbMATH Keywords

Willmore energybending energycatenoidal bridges

Mathematics Subject Classification ID

Global submanifolds (53C40) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05)

Related Items (3)

The Willmore flow with prescribed isoperimetric ratio ⋮ Free boundary minimal annuli immersed in the unit ball ⋮ Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs

Cites Work

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• New examples of conformally constrained Willmore minimizers of explicit type
• Comparison surfaces for the Willmore problem
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere. I
• Existence of surfaces minimizing the Willmore functional
• The catenoid estimate and its geometric applications
• Embedded Delaunay tori and their Willmore energy
• Willmore minimizers with prescribed isoperimetric ratio
• Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint
• Asymptotics of Willmore Minimizers with Prescribed Small Isoperimetric Ratio
• Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II

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