\(L^ 2\) flow of curve straightening in the plane

DOI10.1215/S0012-7094-93-07016-0zbMath0815.58020MaRDI QIDQ1320610

Yingzhong Wen

Publication date: 11 July 1995

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

evolution equationrotation numberconvex curvetotal squared curvaturecurve straightening flow

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear elasticity (74B20) Dynamics induced by flows and semiflows (37C10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Convex sets in (2) dimensions (including convex curves) (52A10) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

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Cites Work

• The total squared curvature of closed curves
• An isoperimetric inequality with applications to curve shortening
• Curve shortening makes convex curves circular
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Geometric theory of semilinear parabolic equations
• Curve straightening and a minimax argument for closed elastic curves
• The influence of elasticity on analysis: The classic heritage
• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• The zero set of a solution of a parabolic equation.
• Some Properties of the Curve Straightening Flow in the Plane
• Analytic Inequalities

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