Faster (than normal) convergence of the normalized Ricci flow on surfaces

Consider a compact surface M of genus γ>1 (I am using the more usual letter “g” to denote metric), and the normalized Ricci flow on it. It is known that at time t, the scalar curvature R satisfies
|Rr|<Cert,
where r=MRdμMdμ is the average scalar curvature of M, and C is a constant depending only on the initial metric g0.

I was wondering if certain special examples are known where the convergence takes place much more quickly under the normalized Ricci flow. For example, a nice answer could be: there is this special surface of genus γ1 with special starting metric g0 such that at time t, we have
|Rr|<Ceert.
Any ideas, references, will be highly appreciated.

Answer

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Source : Link , Question Author : user81712 , Answer Author : Community

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