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