Convex ancient solutions to curve shortening flow

DOI10.1007/s00526-020-01784-8zbMath1446.53071arXiv1903.02022OpenAlexW3043159255MaRDI QIDQ2192934

Giuseppe Tinaglia, Theodora Bourni, Mat Langford

Publication date: 21 August 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02022

zbMATH Keywords

Angenent ovalsconvex ancient solutionsshrinking circles, grim reapers

Mathematics Subject Classification ID

Parabolic equations and parabolic systems (35K99) Flows related to mean curvature (53E10)

Related Items (14)

Uniqueness of convex ancient solutions to hypersurface flows ⋮ Self-similar solutions to the curvature flow and its inverse on the 2-dimensional light cone ⋮ Convexity of 2-convex translating and expanding solitons to the mean curvature flow in \(\mathbb{R}^{n+1}\) ⋮ Collapsing and noncollapsing in convex ancient mean curvature flow ⋮ Aleksandrov reflection for extrinsic geometric flows of Euclidean hypersurfaces ⋮ Classification of convex ancient free-boundary curve-shortening flows in the disc ⋮ Ancient solutions of Ricci flow with type I curvature growth ⋮ Convexity of 2-convex translating solitons to the mean curvature flow in \(\mathbb{R}^{n+1}\) ⋮ Ancient and eternal solutions to mean curvature flow from minimal surfaces ⋮ Ancient solutions to the Curve Shortening Flow spanning the halfplane ⋮ Ancient finite entropy flows by powers of curvature in \(\mathbb{R}^2\) ⋮ Ancient mean curvature flows out of polytopes ⋮ Ancient solutions for flow by powers of the curvature in \(\mathbb{R}^2\) ⋮ Mean curvature flow in null hypersurfaces and the detection of MOTS

Cites Work

• Unnamed Item
• Classification of convex ancient solutions to curve shortening flow on the sphere
• Convex solutions to the mean curvature flow
• On the existence of translating solutions of mean curvature flow in slab regions
• Curve shortening makes convex curves circular
• Asymptotic behavior for singularities of the mean curvature flow
• Classification of compact ancient solutions to the curve shortening flow
• The normalized curve shortening flow and homothetic solutions
• The heat equation shrinking convex plane curves
• Harnack inequalities for evolving hypersurfaces
• Geometric aspects of Aleksandrov reflection and gradient estimates for parabolic equations
• Harnack estimate for the mean curvature flow
• On Harnack's inequality and entropy for the gaussian curvature flow
• A stable manifold theorem for the curve shortening equation
• A deterministic‐control‐based approach motion by curvature
• Aleksandrov reflection and geometric evolution of hypersurfaces

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