Utilizing the Atacama Large Millimeter/submillimeter Array, we present CS line maps in five rotational lines (J u = 7, 5, 4, 3, 2) toward the circumnuclear disk (CND) and streamers of the Galactic center. Our primary goal is to resolve the compact structures within the CND and the streamers, in order to understand the stability conditions of molecular cores in the vicinity of the supermassive black hole (SMBH) Sgr A∗. Our data provide the first homogeneous high-resolution (1.″3 = 0.05 pc) observations aiming at resolving density and temperature structures. The CS clouds have sizes of 0.05-0.2 pc with a broad range of velocity dispersion (σ FWHM = 5-40 km s-1). The CS clouds are a mixture of warm (T k ≥ 50-500 K, nH2 = 103-105 cm-3) and cold gas (T k ≤ 50 K, nH2 = 106-108 cm-3). A stability analysis based on the unmagnetized virial theorem including tidal force shows that 84-37+16% of the total gas mass is tidally stable, which accounts for the majority of gas mass. Turbulence dominates the internal energy and thereby sets the threshold densities 10-100 times higher than the tidal limit at distance ≥1.5 pc to Sgr A∗, and therefore it inhibits the clouds from collapsing to form stars near the SMBH. However, within the central 1 pc, the tidal force overrides turbulence and the threshold densities for a gravitational collapse quickly grow to ≥ 108 cm-3.