  We consider analytically the dynamics of an arbitrary number and
configuration of vortices in an annular Bose-Einstein condensate obtaining
expressions for the free energy and vortex precession rates to logarithmic
accuracy. We also obtain lower bounds for the lifetime of a single vortex in
the annulus. Our results enable a closed-form analytic treatment of
vortex-vortex interactions in the annulus that is exact in the incompressible
limit. The incompressible hydrodynamics that is developed here paves the way
for more general analytical treatments of vortex dynamics in non-simply
connected geometries.
