Nonplanar ancient curve shortening flows in \(\mathbb{R}^3\) from grim reapers

DOI10.1007/S00209-023-03320-8zbMath1527.53082arXiv2201.02134OpenAlexW4385639017MaRDI QIDQ6174832

Theodora Bourni, Alexander Mramor

Publication date: 17 August 2023

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.02134

zbMATH Keywords

ancient solutionscurve shortening flow

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Flows related to mean curvature (53E10)

Cites Work

• Bounding dimension of ambient space by density for mean curvature flow
• Complexity of parabolic systems
• Shortening space curves and flow through singularities
• Collapsing ancient solutions of mean curvature flow
• A planarity estimate for pinched solutions of mean curvature flow
• Ancient solutions to mean curvature flow for isoparametric submanifolds
• Uniqueness and pseudolocality theorems of the mean curvature flow
• The zoo of solitons for curve shortening in $\mathbb{R}^n$
• Ancient solutions to curve shortening with finite total curvature
• Collapsing and noncollapsing in convex ancient mean curvature flow

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