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.
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