  We consider a rapidly rotating Bose-condensed gas in an harmonic plus quartic
trap. At sufficiently high rotation rates the condensate acquires an annular
geometry with the superposition of a vortex lattice. With increasing rotation
rate the lattice evolves into a single ring of vortices. Of interest is the
transition from this state to the giant vortex state in which the circulation
is carried by only a central vortex. By analyzing the Gross-Pitaevskii energy
functional variationally, we have been able to map out the phase boundary
between these two states as a function of the rotation rate and the various
trapped gas parameters. The variational results are in good qualitative
agreement with those obtained by means of a direct numerical solution of the
Gross-Pitaevskii equation.
