Collapsing and noncollapsing in convex ancient mean curvature flow

DOI10.1515/crelle-2023-0045zbMath1521.90040arXiv2106.06339OpenAlexW3172349336WikidataQ125391340 ScholiaQ125391340MaRDI QIDQ6112410

Stephen Lynch, Mat Langford, Theodora Bourni

Publication date: 7 August 2023

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.06339

Mathematics Subject Classification ID

Traffic problems in operations research (90B20)

Related Items

Convexity estimates for high codimension mean curvature flow, Nonplanar ancient curve shortening flows in \(\mathbb{R}^3\) from grim reapers, Uniqueness of entire graphs evolving by mean curvature flow, Ancient solutions of Ricci flow with type I curvature growth

Cites Work

• Unnamed Item
• Unnamed Item
• Type I ancient compact solutions of the Yamabe flow
• Classification of convex ancient solutions to curve shortening flow on the sphere
• Noncollapsing in mean-convex mean curvature flow
• Mean curvature flow of pinched submanifolds to spheres
• Convex solutions to the mean curvature flow
• Classification of ancient compact solutions to the Ricci flow on surfaces
• Flow by mean curvature of convex surfaces into spheres
• Motion of level sets by mean curvature. I
• On the formation of singularities in the curve shortening flow
• Convex ancient solutions of the mean curvature flow
• Interior estimates for hypersurfaces moving by mean curvature
• Classification of compact ancient solutions to the curve shortening flow
• Mean curvature flow with surgeries of two-convex hypersurfaces
• Singularity profile in the mean curvature flow
• Mean curvature flow singularities for mean convex surfaces
• Convexity estimates for mean curvature flow and singularities of mean convex surfaces
• A fully nonlinear flow for two-convex hypersurfaces in Riemannian manifolds
• Type II ancient compact solutions to the Yamabe flow
• Non-collapsing in fully non-linear curvature flows
• Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
• Collapsing ancient solutions of mean curvature flow
• Ancient mean curvature flows out of polytopes
• Singularity models of pinched solutions of mean curvature flow in higher codimension
• A planarity estimate for pinched solutions of mean curvature flow
• Ancient asymptotically cylindrical flows and applications
• Uniqueness of convex ancient solutions to hypersurface flows
• Convex ancient solutions to curve shortening flow
• Uniqueness of two-convex closed ancient solutions to the mean curvature flow
• On the rotational symmetry of 3-dimensional \(\kappa \)-solutions
• Ancient solutions of geometric flows with curvature pinching
• Lagrangian mean curvature flow of Whitney spheres
• The Dirichlet problem for the prescribed curvature equations
• Uniqueness of compact ancient solutions to the higher-dimensional Ricci flow
• Uniqueness of entire graphs evolving by mean curvature flow
• Two-sided non-collapsing curvature flows
• Mean Curvature Flow of Mean Convex Hypersurfaces
• On Brendle’s Estimate for the Inscribed Radius Under Mean Curvature Flow
• The nature of singularities in mean curvature flow of mean-convex sets
• The size of the singular set in mean curvature flow of mean-convex sets
• Extrinsic Geometric Flows
• Ancient gradient flows of elliptic functionals and Morse index
• Strong spherical rigidity of ancient solutions of expansive curvature flows
• On Hypersurfaces with no Negative Sectional Curvatures
• Classification of noncollapsed translators in \(\mathbb{R}^4\)