The Ricci flow on a cylinder
  In this paper we study the Ricci flow on surfaces homeomorphic to a cylinder (that is, a product of the circle with a compact interval). We prove longtime existence results, results on the asymptotic behavior of the flow, and we report on an interesting phenomenon: convergence to constant curvature in the normalised flow,under certain assumptions on the initial data, cannot be exponential. 
Jean Cortissoz and Alexander Murcia
math.DG