ABSTRACT
The monotonicity of volume under contractions of arbitrary arrangements of spheres is a well-known fundamental problem in discrete geometry. The research on this topic started with the conjecture of Poulsen and Kneser in the late 1950s. We survey the status of the long-standing Kneser-Poulsen conjecture in Euclidean as well as in non-Euclidean spaces with emphases on the latest developments.
