Convergence of mean curvature flows with surgery

TL;DR

This paper proves that the surgery process for mean curvature flow on two-convex hypersurfaces converges to the level set flow as the surgery parameter H approaches infinity, establishing a connection between surgical and level set approaches.

Contribution

It demonstrates the convergence of Huisken and Sinestrari's mean curvature flow with surgery to the level set flow in the limit of the surgery parameter H.

Findings

Surgery process converges to level set flow as H approaches infinity

Provides rigorous mathematical proof of convergence

Connects surgical and level set formulations of mean curvature flow

Abstract

Huisken and Sinestrari have recently defined a surgery process for mean curvature flow when the initial data is a two-convex hypersurface. The process depends on a parameter H. Its role is to initiate a surgery when the maximum of the mean curvature of the evolving hypersurface becomes H, and to control the scale at which each surgery is performed. We prove that as H goes to infinity the surgery process converges to level set flow.