  Residual-gas expulsion after cluster formation has recently been shown to
leave an imprint in the low-mass present-day stellar mass function (PDMF) which
allowed the estimation of birth conditions of some Galactic globular clusters
(GCs) such as mass, radius and star formation efficiency. We show that in order
to explain their characteristics (masses, radii, metallicity, PDMF) their
stellar initial mass function (IMF) must have been top-heavy. It is found that
the IMF is required to become more top-heavy the lower the cluster metallicity
and the larger the pre-GC cloud-core density are. The deduced trends are in
qualitative agreement with theoretical expectation. The results are consistent
with estimates of the shape of the high-mass end of the IMF in the Arches
cluster, Westerlund 1, R136 and NGC 3603, as well as with the IMF independently
constrained for ultra-compact dwarf galaxies (UCDs). The latter suggests that
GCs and UCDs might have formed along the same channel or that UCDs formed via
mergers of GCs. A fundamental plane is found which describes the variation of
the IMF with density and metallicity of the pre-GC cloud-cores simultaneously.
The implications for the evolution of galaxies and chemical enrichment over
cosmological times are expected to be major.
