The Kneser-Poulsen conjecture says that if a finite set of (not necessarily congruent) balls in an n-dimensional Euclidean space is rearranged so that the distance between each pair of centers does not increase, then the volume of the union of the balls does not increase as well. We give new results about central sets and apply them to prove new special cases of the Kneser-Poulsen conjecture in the two-dimensional sphere and the hyperbolic plane.