Mean curvature flow with surgery

Abstract

We give a new proof for the existence of mean curvature flow with surgery of 2-convex hypersurfaces in $R^N$, as announced in arXiv:1304.0926. Our proof works for all $N\ge 3$, including mean convex surfaces in $R^3$. We also derive a priori estimates for a more general class of flows in a local and flexible setting.

References in corpus (5)

• Ricci flow with surgery on three-manifolds
• Ricci Flow and the Poincare Conjecture
• The moduli space of two-convex embedded spheres
• Uniqueness of blowups and Lojasiewicz inequalities
• A monotonicity formula for mean curvature flow with surgery

Cited by in corpus (20)

• Uniqueness of convex ancient solutions to mean curvature flow in higher dimensions
• Minimal two-spheres in three-spheres
• The moduli space of two-convex embedded tori
• A nonexistence result for wing-like mean curvature flows in ${\mathbb{R}}^4$
• Approximation of mean curvature flow with generic singularities by smooth flows with surgery
• A fully nonlinear flow for two-convex hypersurfaces
• Mean curvature flow with generic initial data
• Cylindrical Estimates for High Codimension Mean Curvature Flow
• Low Entropy and the Mean Curvature Flow with Surgery
• The extension problem of the mean curvature flow (I)
• On Ilmanen's multiplicity-one conjecture for mean curvature flow with type-I mean curvature
• Lectures on mean curvature flow
• On uniqueness and nonuniqueness of ancient ovals
• On self shrinkers of medium entropy in ${\mathbb{R}}^4$
• Bifurcation of perturbations of non-generic closed self-shrinkers
• Quantitative long range curvature estimate for mean curvature flow
• An unknottedness result for self shrinkers with multiple ends
• On the mean convexity of a space-and-time neighborhood of generic singularities formed by mean curvature flow
• Revisiting generic mean curvature flow in ${\mathbb{R}}^3$
• On the non-degenerate and degenerate generic singularities formed by mean curvature flow