Willmore energy estimates in conformal Berger spheres

DOI10.1016/j.chaos.2011.04.003zbMath1223.53027OpenAlexW2155876558MaRDI QIDQ634928

Manuel Barros, Angel Ferrández

Publication date: 17 August 2011

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2011.04.003

zbMATH Keywords

isoperimetric inequalitiesconformal structuresHopf toriisoareal

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Optimization of shapes other than minimal surfaces (49Q10)

Related Items

On Otsuki tori and their Willmore energy ⋮ Some Variational Problems on Curves and Applications ⋮ Equivariant Willmore surfaces in conformal homogeneous three spaces ⋮ On rigidity phenomena of compact surfaces in homogeneous $3$-manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some results about the existence of critical points for the Willmore functional
• The principle of symmetric criticality
• The total squared curvature of closed curves
• Rotational surfaces in \({\mathbb{L}^3}\) and solutions of the nonlinear sigma model
• Hopf tori in \(S^ 3\)
• Willmore tori and Willmore-Chen submanifolds in pseudo-Riemannian spaces
• The Willmore conjecture in the real projective space
• A geometric algorithm to construct new solitons in the \(O(3)\) nonlinear sigma model
• Existence of surfaces minimizing the Willmore functional
• The fundamental equations of a submersion
• TIME-INDEPENDENT SOLUTIONS TO THE TWO-DIMENSIONAL NONLINEAR O(3) SIGMA MODEL AND SURFACES OF CONSTANT MEAN CURVATURE
• Test fields on compact space-times
• Knotted Elastic Curves in R ³
• Willmore tori in non-standard 3-spheres
• A relation between the right triangle and circular tori with constant mean curvature in the unit 3-sphere
• Lawson-type problems in non-standard 3-spheres
• Classical solutions to the Dirichlet problem for Willmore surfaces of revolution