Gradient flow for the Willmore functional
From MaRDI portal
Publication:1866514
DOI10.4310/CAG.2002.v10.n2.a4zbMath1029.53082MaRDI QIDQ1866514
Reiner Michael Schätzle, Ernst Christoph Kuwert
Publication date: 7 April 2003
Published in: Communications in Analysis and Geometry (Search for Journal in Brave)
Related Items
On the biharmonic heat equation on complete Riemannian manifolds ⋮ Linear and quasilinear parabolic equations in Sobolev space ⋮ The parametric approach to the Willmore flow ⋮ The surface diffusion and the Willmore flow for uniformly regular hypersurfaces ⋮ Branch points of Willmore surfaces ⋮ GRADIENT FLOWS OF HIGHER ORDER YANG–MILLS–HIGGS FUNCTIONALS ⋮ The Willmore boundary problem ⋮ A convergence result for the gradient flow of \(\int|A|^2\) in Riemannian manifolds ⋮ Boundary value problems for the one-dimensional Willmore equation ⋮ A finite element method for surface restoration with smooth boundary conditions ⋮ Unnamed Item ⋮ Short-time existence of the Möbius-invariant Willmore flow ⋮ Flow by mean curvature of slowly rotating liquid drops toward stable energy minimisers ⋮ The geometric triharmonic heat flow of immersed surfaces near spheres ⋮ The gradient flow of the Möbius energy: \(\epsilon\)-regularity and consequences ⋮ Lifespan theorem and gap lemma for the globally constrained Willmore flow ⋮ On the curve diffusion flow of closed plane curves ⋮ A classification theorem for Helfrich surfaces ⋮ Higher order Yang-Mills flow ⋮ Lifespan theorem for simple constrained surface diffusion flows ⋮ A Nested Variational Time Discretization for Parametric Anisotropic Willmore Flow ⋮ Regularity of the obstacle problem for the parabolic biharmonic equation ⋮ Nonlocal flow driven by the radius of curvature with fixed curvature integral ⋮ The obstacle problem for a fourth order semilinear parabolic equation ⋮ Surface diffusion flow of arbitrary codimension in space forms ⋮ Explicit conformally constrained Willmore minimizers in arbitrary codimension ⋮ On the HSL-flow ⋮ “Gradient-free” diffuse approximations of the Willmore functional and Willmore flow ⋮ Gradient flow for the Helfrich functional ⋮ The Willmore flow with prescribed isoperimetric ratio ⋮ Nonlinear questions in clamped plate models ⋮ Global existence and full convergence of the Möbius-invariant Willmore flow in the 3-sphere ⋮ Willmore flow of complete surfaces ⋮ On the convergence of the Willmore flow with Dirichlet boundary conditions ⋮ Surface diffusion flow near spheres ⋮ A NEW HIGHER ORDER YANG–MILLS–HIGGS FLOW ON RIEMANNIAN -MANIFOLDS ⋮ The volume-preserving Willmore flow ⋮ Solutions with single radial interface of the generalized Cahn-Hilliard flow ⋮ Ambient obstruction flow ⋮ Conformal bach flow ⋮ Lifespan theorem for constrained surface diffusion flows ⋮ A dynamical approach to the variational inequality on modified elastic graphs ⋮ Skew mean curvature flow ⋮ The evolution of a class of curve flows ⋮ Feature matching and heat flow in centro-affine geometry ⋮ Embedded surfaces of arbitrary genus minimizing the Willmore energy under isoperimetric constraint ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ The gradient flow of \(\int _M|Rm|^{2}\) ⋮ Analysis aspects of Willmore surfaces ⋮ Phase field models for thin elastic structures with topological constraint ⋮ The gradient flow of the \(L^2\) curvature functional with small initial energy ⋮ A note on singularities in finite time for the \(L^{2}\) gradient flow of the Helfrich functional ⋮ Foliations of asymptotically flat manifolds by surfaces of Willmore type ⋮ Gap phenomena for a class of fourth-order geometric differential operators on surfaces with boundary ⋮ Some results about the existence of critical points for the Willmore functional ⋮ Biharmonic map heat flow into manifolds of nonpositive curvature ⋮ Fourth order approximation of harmonic maps from surfaces ⋮ The area preserving Willmore flow and local maximizers of the Hawking mass in asymptotically Schwarzschild manifolds ⋮ On a curvature flow model for embryonic epidermal wound healing ⋮ FOURTH ORDER GEOMETRIC EVOLUTION EQUATIONS ⋮ Higher-order geometric flow of hypersurfaces in a Riemannian manifold ⋮ Critical weak immersed surfaces within sub-manifolds of the Teichmüller space ⋮ A survey of the elastic flow of curves and networks ⋮ Willmore blowups are never compact ⋮ Isogeometric analysis of geometric partial differential equations ⋮ Finite element methods for fourth order axisymmetric geometric evolution equations ⋮ A Convergent evolving finite element algorithm for Willmore flow of closed surfaces ⋮ Global and local theory of skew mean curvature flows ⋮ Higher order Seiberg-Witten functionals and their associated gradient flows ⋮ Reflection of Willmore Surfaces with Free Boundaries ⋮ A curve flow evolved by a fourth order parabolic equation ⋮ Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations ⋮ Design of Loop's subdivision surfaces by fourth-order geometric PDEs with \(G^1\) boundary conditions ⋮ Stationary points of nonlinear plate theories