Stability of mean convex cones under mean curvature flow

Julie Clutterbuck, Oliver C. Schnürer

Published 2008-11-03Version 1

We consider graphical solutions to mean curvature flow and obtain a stability result for homothetically expanding solutions coming out of cones of positive mean curvature: If another solution is initially close to the cone at infinity, then the difference to the homothetically expanding solution becomes small for large times. The proof involves the construction of appropriate barriers.