On Yau's problem of evolving one curve to another: convex case

DOI10.1016/j.jde.2018.07.037zbMath1403.53004OpenAlexW2883283372WikidataQ129458772 ScholiaQ129458772MaRDI QIDQ1993962

Laiyuan Gao, Yun-tao Zhang

Publication date: 6 November 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.07.037

zbMATH Keywords

convex curveSteiner point\(C^{\infty}\) convergenceYau's curvature difference flow

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Curves in Euclidean and related spaces (53A04)

Related Items (9)

On a length-preserving inverse curvature flow of convex closed plane curves ⋮ The evolution of gradient flow minimizing the anisoperimetric ratio of convex plane curves ⋮ Star-shaped centrosymmetric curves under Gage's area-preserving flow ⋮ Anisotropic area-preserving nonlocal flow for closed convex plane curves ⋮ An anisotropic area-preserving flow and its geometric application ⋮ Two nonlocal inverse curvature flows of convex closed plane curves ⋮ On an area-preserving inverse curvature flow of convex closed plane curves ⋮ An extension of Rabinowitz's polynomial representation for convex curves ⋮ Representation formulae for higher order curvature flows

Cites Work

• Multiphase thermomechanics with interfacial structure. II: Evolution of an isothermal interface
• An isoperimetric inequality with applications to curve shortening
• On the formation of singularities in the curve shortening flow
• On a simple maximum principle technique applied to equations on the circle
• On a non-local curve evolution problem in the plane
• Evolving a convex closed curve to another one via a length-preserving linear flow
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• Four-manifolds with positive curvature operator
• Evolving plane curves by curvature in relative geometries
• Evolving plane curves by curvature in relative geometries. II
• Steiner polynomials, Wulff flows, and some new isoperimetric inequalities for convex plane curves
• Remarks on some isoperimetric properties of the \(k - 1\) flow
• Anisotropic flows for convex plane curves
• Deforming a hypersurface by its Gauss-Kronecker curvature
• Bonnesen-Style Isoperimetric Inequalities
• A convexity theorem for a class of anisotropic flows of plane curves
• Volume preserving anisotropic mean curvature flow
• Positive Centers and the Bonnesen Inequality
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