Precise convergence rates in Ricci flow neckpinches

We examine the formation of cylindrical neckpinch singularities in Ricci flow in compact manifolds. Rigorous examples of neckpinch singularity formation, and examples of degenerate neckpinches with specific asymptotic behaviour have been constructed by Angenent, Knopf and Isenberg. We discuss the asymptotic behaviour of the flow under Type-I assumption for general SO(n)-symmetric initial data, and show the asymptotic profiles mentioned above are the only possibilities.