Some results about the existence of critical points for the Willmore functional

DOI10.1007/s00209-009-0588-6zbMath1205.53046OpenAlexW2126941796MaRDI QIDQ707565

Andrea Mondino

Publication date: 8 October 2010

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-009-0588-6

zbMATH Keywords

scalar curvaturenonlinear elliptic PDEmean curvatureWillmore functionalperturbed method

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Differential geometric aspects of harmonic maps (53C43) Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in infinite-dimensional spaces (58E99)

Related Items (14)

Local solutions to a free boundary problem for the Willmore functional ⋮ ON THE WILLMORE FUNCTIONAL OF 2-TORI IN SOME PRODUCT RIEMANNIAN MANIFOLDS ⋮ Existence of integral \(m\)-varifolds minimizing \(\int |A|^p\) and \(\int |H|^p\), \(p>m\), in Riemannian manifolds ⋮ 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 ⋮ Willmore energy estimates in conformal Berger spheres ⋮ The conformal Willmore functional: a perturbative approach ⋮ On Otsuki tori and their Willmore energy ⋮ Existence of immersed spheres minimizing curvature functionals in non-compact 3-manifolds ⋮ Minimizers of the Willmore functional with a small area constraint ⋮ Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint ⋮ Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds ⋮ Local foliation of manifolds by surfaces of Willmore-type ⋮ Concentration of small Hawking type surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Singularly perturbed elliptic equations with symmetry: existence of solutions concentrating on spheres. I
• The Willmore flow with small initial energy.
• The Willmore flow near spheres.
• Gradient flow for the Willmore functional
• Existence of surfaces minimizing the Willmore functional
• A multiplicity result for the Yamabe problem on \(S^n\)
• Generalized Willmore functionals and related variational problems
• Blow-up phenomena for the Yamabe equation
• Variational perturbative methods and bifurcation of bound states from the essential spectrum
• Partial Differential Equations
• A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
• A Global Invariant of Conformal Mappings in Space
• Geometric properties of QCD string from Willmore functional

This page was built for publication: Some results about the existence of critical points for the Willmore functional