Mean curvature flow with surgery of mean convex surfaces in ${\mathbb{R}}^3$

Abstract

We define a notion of mean curvature flow with surgery for two-dimensional surfaces in ${\mathbb{R}}^3$ with positive mean curvature. Our construction relies on the earlier work of Huisken and Sinestrari in the higher dimensional case. One of the main ingredients in the proof is a new estimate for the inscribed radius established by the first author.

to appear in Invent. Math

References in corpus (2)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Subsequent Singularities in Mean-Convex Mean Curvature Flow

Cited by in corpus (2)

• Two-point functions and their applications in geometry
• Sharp one-sided curvature estimates for mean curvature flow and applications