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In this article we examine the formation of cylindrical neckpinchsingularities in Ricci flow in compact manifolds. Rigorous examples ofneckpinch sigularity for rotationally symmetric initial data were firstconstructed by Angenent and Knopf, and examples with given asymptotic behaviourwere constructed by them and Isenberg. Here we discuss the asymptotic behaviorof the flow under Type-I assumption for general symmetric initial data, andshow the previously constructed asymptotic profiles and are the onlypossibilities.

Exponential Asymptotics of Ricci Flow Neckpinch