  We report results from Monte Carlo simulations of a thin film superconductor
in a spherical geometry within the lowest Landau level approximation. We
observe the absence of a phase transition to a low temperature vortex solid
phase with these boundary conditions; the system remains in the vortex liquid
phase for all accessible temperatures. The correlation lengths are measured for
phase coherence and density modulation. Both lengths display identical
temperature dependences, with an asymptotic scaling form consistent with a
continuous zero temperature transition. This contrasts with the first order
freezing transition which is seen in the alternative quasi-periodic boundary
conditions. The high temperature perturbation theory and the ground states of
the spherical system suggest that the thermodynamic limit of the spherical
geometry is the same as that on the flat plane. We discuss the advantages and
drawbacks of simulations with different geometries, and compare with current
experimental conclusions. The effect of having a large scale inhomogeneity in
the applied field is also considered.
