PUSHING DISKS TOGETHER - THE CONTINUOUS-MOTION CASE

If disks are moved so that each center-center distance does not increa se, must the area of their union also be nonincreasing? We show that t he answer is yes, assuming that there is a continuous motion such that each center-center distance is a nonincreasing function of time. This generalizes a previous result on unit disks. Our proof relies on a re cent construction of Edelsbrunner and on new isoperimetric inequalitie s of independent interest. We go on to show analogous results for the intersection and for holes between disks.