  In this paper, we shall use the K\"ahler geometry formulation to study the
global behavior of the Ricci flow on $R^2$. The geometric feature of our Ricci
flow is that it has finite width. Our aim is to determine the limiting metric
(which corresponds an eternal Ricci flow) obtained by L.F.Wu. We can use the
classification result of Daskalopoulos-Sesum to give a sufficient condition
such that the limiting metric of L.F.Wu is the metric of cigar soliton.
