Energy quantization for Willmore surfaces and applications

DOI10.4007/annals.2014.180.1.2zbMath1325.53014arXiv1106.3780OpenAlexW2129411956MaRDI QIDQ2251002

Tristan Rivière, Yann Bernard

Publication date: 10 July 2014

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.3780

zbMATH Keywords

blow-upmoduli spaceWillmore functionalWillmore surfacestrong compactnessenergy quantization

Mathematics Subject Classification ID

Related Items (30)

The parametric approach to the Willmore flow ⋮ Uniform regularity results for critical and subcritical surface energies ⋮ Noether's theorem and the Willmore functional ⋮ Some remarks on Willmore surfaces embedded in \(\mathbb R^3\) ⋮ The Classification of Branched Willmore Spheres in the 3-Sphere and the 4-Sphere ⋮ An \(\varepsilon\)-regularity result with mean curvature control for Willmore immersions and application to minimal bubbling. ⋮ Global estimates and energy identities for elliptic systems with antisymmetric potentials ⋮ Willmore minmax surfaces and the cost of the sphere eversion ⋮ Analysis of constrained Willmore surfaces ⋮ Minimal Ws,ns$W^{s,\frac{n}{s}}$‐harmonic maps in homotopy classes ⋮ Energy estimates for the tracefree curvature of Willmore surfaces and applications ⋮ Analysis of the inhomogeneous Willmore equation ⋮ Two-dimensional curvature functionals with superquadratic growth ⋮ Global Conformal Invariants of Submanifolds ⋮ Geometric rigidity for sequences of \(W^{2,2}\) conformal immersions ⋮ Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint ⋮ The Variations of Yang–Mills Lagrangian ⋮ A viscosity method in the min-max theory of minimal surfaces ⋮ Variational problems in the theory of hydroelastic waves ⋮ Energy gap for Yang-Mills connections. II: Arbitrary closed Riemannian manifolds ⋮ WEIERSTRASS–KENMOTSU REPRESENTATION OF WILLMORE SURFACES IN SPHERES ⋮ Energy quantization of Willmore surfaces at the boundary of the moduli space ⋮ The Viscous Surface Wave Problem with Generalized Surface Energies ⋮ On the Morse index of branched Willmore spheres in 3-space ⋮ Willmore surfaces with nonremovable singularities and number of critical levels ⋮ Limits of conformal immersions under a bound on a fractional normal curvature quantity ⋮ Problem analysis according to invariants ⋮ Elastic curves and phase transitions ⋮ Existence for Willmore surfaces of revolution satisfying non-symmetric Dirichlet boundary conditions ⋮ Pointwise expansion of degenerating immersions of finite total curvature

Cites Work

• \(W^{2,2}\)-conformal immersions of a closed Riemann surface into \(\mathbb{R}^n\)
• Estimation of the conformal factor under bounded Willmore energy
• Minimizers of the Willmore functional under fixed conformal class
• Singularity removability at branch points for Willmore surfaces
• Local Palais-Smale sequences for the Willmore functional
• Variational principles for immersed surfaces with \(L^2\)-bounded second fundamental form
• Bubble tree convergence for harmonic maps
• A duality theorem for Willmore surfaces
• Boundary regularity and the Dirichlet problem for harmonic maps
• Harmonic maps from degenerating Riemann surfaces
• Analysis aspects of Willmore surfaces
• On the evolution of harmonic mappings of Riemannian surfaces
• The existence of minimal immersions of 2-spheres
• Removability of point singularities of Willmore surfaces
• Geometric conditions and existence of bi-Lipschitz parameterizations
• Energy quantization for harmonic maps
• Interpolation spaces and energy quantization for Yang-Mills fields
• Existence of surfaces minimizing the Willmore functional
• Energy identity for a class of approximate harmonic maps from surfaces
• On surfaces of finite total curvature
• Min-max theory and the Willmore conjecture
• Angular energy quantization for linear elliptic systems with antisymmetric potentials and applications
• Noether's theorem and the Willmore functional
• A remark on generalized harmonic maps into spheres
• Willmore two-spheres in the four-sphere
• A Quantization Property for Moving Line Vortices
• Lipschitz conformal immersions from degenerating Riemann surfaces with L2-bounded second fundamental forms
• Closed surfaces with bounds on their Willmore energy
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Energy quantization for Willmore surfaces and applications