The conformal Willmore functional: a perturbative approach

DOI10.1007/s12220-011-9263-3zbMath1276.53068arXiv1010.4151OpenAlexW1967461839MaRDI QIDQ1948732

Andrea Mondino

Publication date: 24 April 2013

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.4151

zbMATH Keywords

nonlinear elliptic PDEmean curvatureconformal geometryWillmore functionalperturbative method

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20) Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.) (58J60) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in infinite-dimensional spaces (58E99)

Related Items (7)

On shape dependence of holographic entanglement entropy in \(\mathrm{AdS}_{4}/CFT_{3}\) ⋮ A convergence result for the gradient flow of \(\int|A|^2\) in Riemannian manifolds ⋮ Some rigidity results for the Hawking mass and a lower bound for the Bartnik capacity ⋮ Global Conformal Invariants of Submanifolds ⋮ Minimizers of the Willmore functional with a small area constraint ⋮ Embedded loops in the hyperbolic plane with prescribed, almost constant curvature ⋮ Local foliation of manifolds by surfaces of Willmore-type

Cites Work

• Some results about the existence of critical points for the Willmore functional
• Perturbation methods and semilinear elliptic problems on \(\mathbb R^n\)
• Analysis aspects of Willmore surfaces
• Constant mean curvature spheres in Riemannian manifolds
• Homoclinics: Poincaré-Melnikov type results via a variational approach
• Removability of point singularities of Willmore surfaces
• New examples of Willmore surfaces in \(S^n\)
• Existence of surfaces minimizing the Willmore functional
• Generalized Willmore functionals and related variational problems
• Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
• Variational perturbative methods and bifurcation of bound states from the essential spectrum
• Riemannian Geometry
• The second variational formula for Willmore submanifolds in \(S^n\).
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