Define Hamilton's Ricci flow as $$\frac{\partial}{\partial t} g_{ij}(t) = -2 R_{ij}(t)$$
Q: Does there exist a regularized Ricci flow like
$$\frac{\partial}{\partial t} g_{ij} = -2 F(g_{ij}, R_{ij})R_{ij}$$
Such that the singularity like neckpinch will not occur during the evolution?