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In this paper we prove local results for solutions to the Ricci flow (heatflow) whose speed (height) is bounded by $\frac c t$ for some time interval $ t\in (0,T)$. These results are contained in chapter 7 of the author'shabilitation thesis, University of Freiburg, Germany, 2006.

Local results for flows whose speed or height satisfies a bound of the form $\frac c t$