On the minimum distance between masses of relative equilibria of the   $n$-body problem
  We prove that if for relative equilibrium solutions of a generalisation of the $n$-body problem of celestial mechanics the masses and rotation are given, then the minimum distance between the point masses of such a relative equilibrium has a universal lower bound that is not equal to zero. We furthermore prove that the set of such relative equilibria is compact. 
Pieter Tibboel
math.DS