  We present the first systematic study of the density structure of clouds
found in a complete sample covering all major molecular clouds in the Central
Molecular Zone (CMZ; inner $\sim{}200~\rm{}pc$) of the Milky Way. This is made
possible by using data from the Galactic Center Molecular Cloud Survey (GCMS),
the first study resolving all major molecular clouds in the CMZ at
interferometer angular resolution. We find that many CMZ molecular clouds have
unusually shallow density gradients compared to regions elsewhere in the Milky
Way. This is possibly a consequence of weak gravitational binding of the
clouds. The resulting relative absence of dense gas on spatial scales
$\sim{}0.1~\rm{}pc$ is probably one of the reasons why star formation (SF) in
dense gas of the CMZ is suppressed by a factor $\sim{}10$, compared to solar
neighborhood clouds. Another factor suppressing star formation are the high SF
density thresholds that likely result from the observed gas kinematics.
Further, it is possible but not certain that the star formation activity and
the cloud density structure evolve systematically as clouds orbit the CMZ.
