The mean curvature at the first singular time of the mean curvature flow

DOI10.1016/j.anihpc.2010.09.002zbMath1237.53067arXiv1001.3682OpenAlexW2139115700MaRDI QIDQ619858

Natasa Sesum, Nam Q. Le

Publication date: 18 January 2011

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3682

zbMATH Keywords

Gaussian densityclosed hypersurfacesmultiplicity one conjecture

Mathematics Subject Classification ID

Related Items (13)

On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-\(I\) mean curvature ⋮ Mean Curvature Flow in Higher Codimension: Introduction and Survey ⋮ Blow-up of the mean curvature at the first singular time of the mean curvature flow ⋮ Extension of two-dimensional mean curvature flow with free boundary ⋮ Existence of mean curvature flow singularities with bounded mean curvature ⋮ Blow up of subcritical quantities at the first singular time of the mean curvature flow ⋮ Partial regularity at the first singular time for hypersurfaces evolving by mean curvature ⋮ Remarks on the extension of the Ricci flow ⋮ Analysis of Velázquez’s solution to the mean curvature flow with a type II singularity ⋮ Mixed integral norms for Ricci flow ⋮ A rigidity theorem on the second fundamental form for self-shrinkers ⋮ The extension problem of the mean curvature flow (I) ⋮ A local estimate for the mean curvature flow

Cites Work

• Unnamed Item
• Unnamed Item
• Generic mean curvature flow. I: Generic singularities
• Extend mean curvature flow with finite integral curvature
• A note on singular time of mean curvature flow
• The extension for mean curvature flow with finite integral curvature in Riemannian manifolds
• Flow by mean curvature of convex surfaces into spheres
• A local regularity theorem for mean curvature flow
• Asymptotic behavior for singularities of the mean curvature flow
• Interior estimates for hypersurfaces moving by mean curvature
• Lower semicontinuity of the Willmore functional for currents
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• Contracting convex hypersurfaces in Riemannian manifolds by their mean curvature
• Mean curvature flow singularities for mean convex surfaces
• On regularity for mean curvature flow of hypersurfaces
• A density function and the structure of singularities of the mean curvature flow
• Starshaped hypersurfaces and the mean curvature flow
• Regularity theory for mean curvature flow
• The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks
• On the extension of the mean curvature flow
• On the Convergence of the Ohta–Kawasaki Equation to Motion by Nonlocal Mullins–Sekerka Law
• A characterization of the singular time of the mean curvature flow
• On stable complete minimal hypersurfaces in R n +1
• The Motion of a Surface by Its Mean Curvature. (MN-20)
• Stratification of minimal surfaces, mean curvature flows, and harmonic maps.
• The size of the singular set in mean curvature flow of mean-convex sets

This page was built for publication: The mean curvature at the first singular time of the mean curvature flow