A gap theorem for Willmore tori and an application to the Willmore flow

DOI10.1016/j.na.2014.02.015zbMath1286.53012arXiv1308.4238OpenAlexW2005249660MaRDI QIDQ2443042

Andrea Mondino, Huy The Nguyen

Publication date: 4 April 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1308.4238

zbMATH Keywords

Willmore functionalgeometric flowssurface theorynonlinear elliptic equation of 4th order

Mathematics Subject Classification ID

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Cites Work

• A duality theorem for Willmore surfaces
• Analysis aspects of Willmore surfaces
• Willmore blowups are never compact
• Hopf tori in \(S^ 3\)
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• The Willmore flow with small initial energy.
• Removability of point singularities of Willmore surfaces
• Existence of surfaces minimizing the Willmore functional
• Min-max theory and the Willmore conjecture
• The large genus limit of the infimum of the Willmore energy
• Willmore two-spheres in the four-sphere
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