  We prove that any hyperbolic end with particles (cone singularities along
infinite curves of angles less than $\pi$) admits a unique foliation by
constant Gauss curvature surfaces. Using a form of duality between hyperbolic
ends with particles and convex globally hyperbolic maximal (GHM) de Sitter
spacetime with particles, it follows that any convex GHM de Sitter spacetime
with particles also admits a unique foliation by constant Gauss curvature
surfaces. We prove that the grafting map from the product of Teichm\"uller
space with the space of measured laminations to the space of complex projective
structures is a homeomorphism for surfaces with cone singularities of angles
less than $\pi$, as well as an analogue when grafting is replaced by "smooth
grafting".
