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We show that any integral Brakke flow coming out of a rotationally symmetricdouble cone with entropy at most two must stay rotationally symmetric for alltime, provided the flow is smooth for a short time. We also show the existenceof a non-self-similar flow coming out of a double cone with entropy at mosttwo, and give an example of such a flow with a finite time singularity.

Rotational symmetry of solutions of mean curvature flow coming out of a double cone II