Deforming locally convex curves into curves of constant \(k\)-order width

DOI10.1016/J.DIFGEO.2024.102192MaRDI QIDQ6654679

Deyan Zhang, Horst Martini, Laiyuan Gao

Publication date: 20 December 2024

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

curvature flowlocally convex curveBlaschke-Lebesgue problemcurves of constant \(k\)-order width

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Convex sets in (2) dimensions (including convex curves) (52A10) Curves in Euclidean and related spaces (53A04) Flows related to mean curvature (53E10)

Cites Work

• Evolving convex curves to constant-width ones by a perimeter-preserving flow
• Evolving a convex closed curve to another one via a length-preserving linear flow
• The normalized curve shortening flow and homothetic solutions
• Evolving convex curves to constant \(k\)-order width ones by a perimeter-preserving flow
• On Yau's problem of evolving one curve to another: convex case
• Representation formulae for higher order curvature flows
• Area-preserving evolution of nonsimple symmetric plane curves
• Length-preserving evolution of immersed closed curves and the isoperimetric inequality
• Analytic parametrization of three-dimensional bodies of constant width
• The curve shortening problem
• Self-similar solutions to the curve shortening flow
• On the three-dimensional Blaschke-Lebesgue problem
• Evolving convex surfaces to constant width ones
• Bodies of Constant Width
• Evolution of non-simple closed curves in the area-preserving curvature flow
• Whitney-Graustein homotopy of locally convex curves via a curvature flow

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