  We consider Ricci flow on a closed surface with cone points. The main result
is: given a (nonsmooth) cone metric g_0 over a closed surface there is a smooth
Ricci flow g(t) defined for (0,T], with curvature unbounded above, such that
g(t) tends to g_0 as t tends to 0. This result means that Ricci flow provides a
way for instantaneously smoothening cone points. We follow an argument of P.
Topping modifying his reasoning for cusps of negative curvature; in that sense
we can consider cusps as a limiting zero-angle cone, and we generalize to any
angle between 0 and 2\pi.
