Kinetic equilibration of the matter and baryon densities attained in central region of colliding Au+Au nuclei in the energy range of √ sNN = 3.3-39 GeV are examined within the model of the three-fluid dynamics. It is found that the kinetic equilibration is faster at higher collision energies: the equilibration time (in the c.m. frame of colliding nuclei) rises from ∼5 fm/c at √ sNN = 3.3 GeV to ∼1 fm/c at 39 GeV. The chemical equilibration, and thus thermalization, takes longer. We argue that for informative comparison of predictions of different models it is useful to calculate an invariant 4-volume (V4), where the proper density the equilibrated matter exceeds certain value. The advantage of this 4-volume is that it does not depend on specific choice of the 3-volume in different studies and takes into account the lifetime of the high-density region, which also matters. The 4-volume V4 = 100 fm 4 /c is chosen to compare the baryon densities attainable at different different energies. It is found that the highest proper baryon density increases with the collision energy rise, from nB/n0 ≈ 4 at 3.3 GeV to nB/n0 ≈ 30 at 39 GeV. These highest densities are achieved in the central region of colliding system.