Wandering singularities

Parabolic geometric flows are smoothing for short time however, over long time, singularities typically unavoidable, can be very nasty and may impossible to classify. The idea of [CM6] here is that, by bringing in the dynamical properties flow, we obtain also large generic initial conditions. When combined with [CM1], this shows, an important special case, simplest possible. question dynamics a singularity has two parts. One is: What near singularity? second behavior? That is, if flow leaves neighborhood singularity, it return at much later time? first was addressed here. Combined [CM6], show that all other closed than (round) sphere have where “nearly every” hypersurface under never returns, even dilated, rotated or translated copy singularity. In words, wanders off. contrast, Huisken, any remains close dilated each time.