Cartan-decomposition subgroups of SU(2,n)
  We give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G = SU(2,n) has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = K A K of G, and then carry out an approximate calculation of the intersection of KHK with A, for each closed, connected subgroup H of G. This generalizes the work of Hee Oh and Dave Witte for G = SO(2,n). 
Alessandra Iozzi and Dave Witte