Willmore flow of complete surfaces

DOI10.1016/J.JFA.2023.110284arXiv2212.08692OpenAlexW4389670398MaRDI QIDQ6146580

Long-Sin Li

Publication date: 15 January 2024

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.08692

zbMATH Keywords

asymptotic behaviorimmersed surfacesshort-time existenceWillmore flow

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Surfaces in Euclidean and related spaces (53A05) PDEs on manifolds (35R01) Flows related to mean curvature (53E10)

Cites Work

• Unnamed Item
• A classification theorem for Helfrich surfaces
• Finite time singularities for the locally constrained Willmore flow of surfaces
• Lifespan theorem for simple constrained surface diffusion flows
• Lifespan theorem for constrained surface diffusion flows
• Willmore blowups are never compact
• A compactness theorem for surfaces with \(L_ p\)-bounded second fundamental form
• A numerical scheme for axisymmetric solutions of curvature-driven free boundary problems, with applications to the Willmore flow
• The Willmore flow with small initial energy.
• Removability of point singularities of Willmore surfaces
• Gradient flow for the Willmore functional
• Existence of surfaces minimizing the Willmore functional
• The parametric approach to the Willmore flow
• Surface diffusion flow near spheres
• The volume-preserving Willmore flow
• A singular example for the Willmore flow
• A note on quasilinear parabolic equations on manifolds
• Asymptotic Estimates for the Willmore Flow With Small Energy
• Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ

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