  We show that the perimeter of the convex hull of finitely many disks lying in
the hyperbolic or Euclidean plane, or in a hemisphere does not increase when
the disks are rearranged so that the distances between their centers do not
increase. This generalizes the theorem on the monotonicity of the perimeter of
the convex hull of a finite set under contractions, proved in the Euclidean
plane by V. N. Sudakov, R. Alexander, V. Capoyleas and J. Pach. We also prove
that the area of the intersection of finitely many disks in the hyperbolic
plane does not decrease after such a contractive rearrangement. The Euclidean
analogue of the latter statement was proved by K. Bezdek and R. Connelly. Both
theorems are proved by a suitable adaptation of a recently published method of
I. Gorbovickis.
