Ricci flow on surfaces with cusps

We consider the normalized Ricci flow ? _t g = (ρ ? R)g with initial condition a complete metric g ₀ on an open surface M where M is conformal to a punctured compact Riemann surface and g ₀ has ends which are asymptotic to hyperbolic cusps. We prove that when χ(M) < 0 and ρ < 0, the flow g(t) converges exponentially to the unique complete metric of constant Gauss curvature ρ/2 in the conformal class.