  A rotating superfluid such as a Bose-Einstein condensate is usually described
by the Gross-Pitaevskii (GP) model. An important issue is to determine from
this model the properties of the quantized vortices that a superfluid nucleates
when set into rotation. In this paper we address the minimization of a two
dimensional GP energy functional describing a rotating annular Bose-Einstein
condensate. In a certain limit it is physically relevant to restrict the
minimimization to the Lowest-Landau-Level, that is the first eigenspace of the
Ginzburg-Landau operator. Taking the particular structure of this space into
account we obtain theoretical results concerning the vortices of the
condensate. We also compute the vortices' locations by a numerical minimization
procedure. We find that they lie on a distorted lattice and that multiply
quantized vortices appear in the central hole of low matter density.
