Asymptotic closeness to limiting shapes for expanding embedded plane curves

DOI10.1007/s00222-005-0449-9zbMath1083.35040OpenAlexW2167951643MaRDI QIDQ2574965

Dong-Ho Tsai

Publication date: 5 December 2005

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-005-0449-9

zbMATH Keywords

asymptotic shapeexpansion speedisoperimetric difference

Mathematics Subject Classification ID

Related Items (9)

Application of Andrews and Green-Osher inequalities to nonlocal flow of convex plane curves ⋮ On a length preserving curve flow ⋮ Using Aleksandrov reflection to estimate the location of the center of expansion ⋮ ON A CURVE EXPANDING FLOW WITH A NON-LOCAL TERM ⋮ Higher order Wirtinger-type inequalities and sharp bounds for the isoperimetric deficit ⋮ On a non-local perimeter-preserving curve evolution problem for convex plane curves ⋮ On a non-local area-preserving curvature flow in the plane ⋮ Evolving a convex closed curve to another one via a length-preserving linear flow ⋮ Contracting convex immersed closed plane curves with slow speed of curvature

Cites Work

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• The heat equation shrinking convex plane curves
• An expansion of convex hypersurfaces
• Evolving convex curves
• Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
• Non-convergence and instability in the asymptotic behaviour of curves evolving by curvature
• Expansion of embedded curves with turning angle greater than \(-\pi\)
• Geometric expansion of starshaped plane curves

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