Convergence of mean curvature flows with surgery

Huisken and Sinestrari have recently defined a surgery process for mean curvature flow when the initial data are a two-convex hypersurface in $R^{n+1}$ ($n\geq 3$). 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 $H\to\infty$ the surgery process converges to level set flow.

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Published 9 April 2013