  We study the initial mass function (IMF) of one of the most massive Galactic
star-forming regions NGC 3603 to answer a fundamental question in current
astrophysics: is the IMF universal, or does it vary? Using our very deep, high
angular resolution JHKsL' images obtained with NAOS-CONICA at the VLT at ESO,
we have successfully revealed the stellar population down to the subsolar mass
range in the core of the starburst cluster. The derived IMF of NGC 3603 is
reasonably fitted by a single power law with index Gamma ~ -0.74 within a mass
range of 0.4 - 20 Msun, substantially flatter than the Salpeter-like IMF. A
strong radial steepening of the IMF is observed mainly in the inner r < 30''
field, indicating mass segregation in the cluster center. We estimate the total
mass of NGC 3603 to be about 1.0 - 1.6 x 10^4 Msun. The derived core density is
> 6 x 10^4 Msun pc^-3, an order of magnitude larger than e.g., the Orion Nebula
Cluster. The estimate of the half-mass relaxation time for solar-mass stars is
about 10 - 40 Myr, suggesting that the intermediate- and low-mass stars have
not yet been affected significantly by the dynamical relaxation in the cluster.
The relaxation time for the high-mass stars can be comparable to the age of the
cluster. We estimate that the stars residing outside the observed field cannot
steepen the IMF significantly, indicating our IMF adequately describes the
whole cluster. Analyzing thoroughly the systematic uncertainties in our IMF
determination, we conclude that the power law index of the IMF of NGC 3603 is
Gamma = -0.74^{+0.62}_{-0.47}. Our result thus supports the hypothesis of a
potential top-heavy IMF in massive star-forming clusters and starbursts.
