Convexity estimates for mean curvature flow with free boundary
Abstract
We prove the convexity estimates of Huisken-Sinestrari for finite-time singularities of mean-convex, mean curvature flow with free boundary in a barrier S. Here S can be any properly embedded, oriented surface in Rn+1 of bounded geometry. We also give an alternative proof that convex mean curvature flows with free boundary in Sn pinch to umbilic.
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