On a perimeter-preserving plane curve flow

DOI10.1007/s11766-001-0009-zzbMath0994.35051OpenAlexW125994001MaRDI QIDQ5953361

Shengliang Pan

Publication date: 25 September 2002

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-001-0009-z

zbMATH Keywords

convex curveconvergence to a circleplanar flow

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (3)

A family of evolution equations connecting area-preserving to length-preserving curve flows ⋮ On some simple examples of non-parabolic curve flows in the plane ⋮ Some remarks about the area-preserving convex curve flow in the plane

Cites Work

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• Geometric expansion of convex plane curves
• Flow by mean curvature of convex surfaces into spheres
• An isoperimetric inequality with applications to curve shortening
• Curve shortening makes convex curves circular
• Asymptotic behavior for singularities of the mean curvature flow
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Evolving convex curves
• Volume-preserving mean curvature flow of rotationally symmetric surfaces
• Mean curvature flow through singularities for surfaces of rotation
• Geometric expansion of starshaped plane curves
• Deforming a hypersurface by its Gauss-Kronecker curvature
• The volume preserving mean curvature flow.
• Bonnesen-Style Isoperimetric Inequalities

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