  The recent Bose-Einstein condensation of ultracold atoms with attractive
interactions led us to consider the novel possibility to probe the stability of
its ground state in arbitrary three-dimensional harmonic traps. We performed a
quantitative analysis of the critical number of atoms through a full numerical
solution of the mean field Gross-Pitaevskii equation. Characteristic limits are
obtained for reductions from three to two and one dimensions, in perfect
cylindrical symmetries as well as in deformed ones.
