On some simple methods to derive the hairclip and paperclip solutions of the curve shortening flow

DOI10.1007/s10473-019-0616-5zbMath1499.53014OpenAlexW2981374950MaRDI QIDQ2151024

Dong-Ho Tsai, Xiao-Liu Wang

Publication date: 30 June 2022

Published in: Acta Mathematica Scientia. Series B. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10473-019-0616-5

zbMATH Keywords

curve shortening flowgrim reaper solutionhairclip solutionpaperclip solution

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15) Curves in Euclidean and related spaces (53A04) Geometric evolution equations (53E99)

Related Items (2)

The fundamental solutions of the curve shortening problem via the Schwarz function ⋮ On an asymptotically log-periodic solution to the graphical curve shortening flow equation

Cites Work

• A comparison theorem for the isoperimetric profile under curve-shortening flow
• The role of symmetry and separation in surface evolution and curve shortening
• On the formation of singularities in the curve shortening flow
• Integrable model of boundary interaction: the paperclip
• Mean curvature evolution of entire graphs
• Classification of compact ancient solutions to the curve shortening flow
• The heat equation shrinking convex plane curves
• The heat equation shrinks embedded plane curves to round points
• Separation of variables for the 1-dimensional nonlinear diffusion equation
• Models of phase transitions
• Integrable equations arising from motions of plane curves
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