Stability of mean convex cones under mean curvature flow
The authors consider graphical solutions to the mean curvature flow and obtain a stability result for homothetically expanding solutions coming out of cones of positive mean curvature. They prove that, if a solution is initially close to the cone near infinity, then this solution will converge uniformly to the homothetically expanding solution in \(C^j\) for any \(j\in\mathbb{N}\) as time increases to infinity. The proof is based on the construction of appropriate barrier functions.
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