Dynamics of closed singularities

Understand

Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify.

• The idea of this paper is that, by bringing in the dynamical properties of the flow, we obtain also smoothing for long time for generic initial conditions.
• When combined with our earlier paper this allows us to show that, in an important special case, the singularities are the simplest possible.
• We take here the first steps towards understanding the dynamics of the flow.