Ancient solutions to curve shortening with finite total curvature

DOI10.1090/tran/8186zbMath1458.53006arXiv1803.01399OpenAlexW3033601432MaRDI QIDQ5143146

Qian You, Sigurd B. Angenent

Publication date: 11 January 2021

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.01399

zbMATH Keywords

total curvaturecurve shortening

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Geometric evolution equations (53E99)

Related Items (5)

Nonconvex ancient solutions to curve shortening flow ⋮ Nonplanar ancient curve shortening flows in \(\mathbb{R}^3\) from grim reapers ⋮ Ancient and eternal solutions to mean curvature flow from minimal surfaces ⋮ Ancient solutions to the Curve Shortening Flow spanning the halfplane ⋮ Ancient mean curvature flows out of polytopes

Cites Work

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• Classification of compact ancient solutions to the curve shortening flow
• The heat equation shrinks embedded plane curves to round points
• Parabolic equations for curves on surfaces. I: Curves with \(p\)-integrable curvature
• Motion of level sets by mean curvature. III
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Curve Lengthening Equation and Its Solutions
• The zoo of solitons for curve shortening in $\mathbb{R}^n$
• Soliton solutions for the mean curvature flow

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