2\(\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem

DOI10.1007/s00526-010-0375-6zbMath1232.34069OpenAlexW1996979932MaRDI QIDQ543394

Liping Wang, Mei Yue Jiang, Wei, Juncheng

Publication date: 17 June 2011

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-010-0375-6

zbMATH Keywords

existenceperiodic solutionsa priori estimatesLyapunov-Schmidt reductiondegree theoryblow-upscurve shortening problemrepulsive type singularity

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Applications of operator theory to differential and integral equations (47N20)

Related Items (20)

On the 2-dimensional dual Minkowski problem ⋮ A unified flow approach to smooth, even \(L_p\)-Minkowski problems ⋮ Mirror symmetric solutions to the centro-affine Minkowski problem ⋮ Multiple solutions of the planar \(L_p\) dual Minkowski problem ⋮ Blowup analysis for a nonlinear equation with negative exponent ⋮ On the positive solutions for a perturbed negative exponent problem on \(\mathbb{R}^3\) ⋮ Variational analysis of the planar \(L_p\) dual Minkowski problem ⋮ Existence of convex hypersurfaces with prescribed centroaffine curvature ⋮ The Christoffel problem in the hyperbolic plane ⋮ A generalized rotationally symmetric case of the centroaffine Minkowski problem ⋮ A remark on rotationally symmetric solutions to the centroaffine Minkowski problem ⋮ Blowup analysis for integral equations on bounded domains ⋮ \(2\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem. II ⋮ Topological degree method for the rotationally symmetric \(L_p\)-Minkowski problem ⋮ Nonexistence of maximizers for the functional of the centroaffine Minkowski problem ⋮ On a nonlinear parabolic equation arising from anisotropic plane curve evolution ⋮ The Orlicz-Minkowski problem for polytopes ⋮ Variational characterization for the planar dual Minkowski problem ⋮ On the planar $L_p$ Minkowski problem with sign-changing data ⋮ An inequality for the minimum affine curvature of a plane curve

Cites Work

• Unnamed Item
• Unnamed Item
• Prescribing Gaussian curvature on \(S^ 2\)
• Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
• On the formation of singularities in the curve shortening flow
• Prescribing \(Q\)-curvature problem on \(S^n\)
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• Prescribing Gaussian curvature on S 2
• The heat equation shrinks embedded plane curves to round points
• A perturbation result in prescribing scalar curvature on \(S^ n\)
• Singularities of the curve shrinking flow for space curves
• On conformal deformations of metrics on \(S^n\)
• Evolving convex curves
• The scalar curvature equation on 2- and 3-spheres
• Evolving plane curves by curvature in relative geometries
• On affine plane curve evolution
• On Nirenberg's problem and related topics
• Evolving plane curves by curvature in relative geometries. II
• Selfsimilar shrinking curves for anisotropic curvature flow equations
• A priori estimates for prescribing scalar curvature equations
• On the uniqueness of stable ultimate shapes for the anisotropic curve-shortening problem
• Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. I: \(N=3\)
• Existence of selfsimilar shrinking curves for anisotropic curvature flow equations
• Contraction of convex hypersurfaces by their affine normal
• Anisotropic flows for convex plane curves
• \(L_p\) Minkowski problem with not necessarily positive data
• Blowing up solutions for an elliptic Neumann problem with sub- or supercritical nonlinearity. II: \(N\geqslant 4\)
• Scalar Curvatures on S 2
• T-periodic solutions for some second order differential equations with singularities
• Remarks on Prescribing Gauss Curvature
• Remarks on the 2-Dimensional L_p-Minkowski Problem
• ON NIRENBERG'S PROBLEM
• Self-similar solutions for the anisotropic affine curve shortening problem

This page was built for publication: 2\(\pi\)-periodic self-similar solutions for the anisotropic affine curve shortening problem