 
Summary: PRECISE ASYMPTOTICS OF THE RICCI FLOW
NECKPINCH
SIGURD ANGENENT & DAN KNOPF
1. Introduction
1.1. Antecedents. In virtually all known applications of the Ricci flow, it
is valuable to have a good understanding of singularity formation. Heuristi
cally, there are at least three reasons for this. The first is that one expects
finitetime singularities to form for a broad spectrum of initial data. Indeed,
such singularities are inevitable if the scalar curvature is strictly positive.
The second reason is that one expects the geometry of a solution to resem
ble a standard model (for example, a selfsimilar solution) in a spacetime
neighborhood of a developing singularity. The third reason is that hav
ing a sufficiently detailed picture of a developing singularity facilitates the
geometrictopological surgeries by which Ricci flow decomposes a given man
ifold.
Whenever a compact solution (Mn, g(·)) of Ricci flow encounters a singu
larity at time T < , standard shorttime existence results imply that
lim
tT
max
