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PRECISE ASYMPTOTICS OF THE RICCI FLOW SIGURD ANGENENT & DAN KNOPF
 

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
finite-time 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 self-similar solution) in a space-time
neighborhood of a developing singularity. The third reason is that hav-
ing a sufficiently detailed picture of a developing singularity facilitates the
geometric-topological 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 short-time existence results imply that
lim
tT
max

  

Source: Angenent, Sigurd - Department of Mathematics, University of Wisconsin at Madison

 

Collections: Mathematics