In this paper, we answer a question raised by Len Pitaevskii and prove that
the ground state of the Gross-Pitaevskii energy describing a Bose Einstein
condensate at low rotation does not have vortices in the low density region.
Therefore, the first ground state with vortices has its vortices in the bulk.
This is obtained by proving that for small rotational velocities, the ground
state is multiple of the ground state with zero rotation. We rely on sharp
bounds of the decay of the wave function combined with weighted jacobian
estimates.