Communications in Analysis and Geometry

Volume 21 (2013)

Number 2

Convergence of mean curvature flows with surgery

Pages: 355 – 363



Joseph Lauer (Department of Mathematics, Yale University, New Haven, Conn., U.S.A.)


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.

Published 9 April 2013