  We analyse the secular effects of a long-lived Galactic spiral structure on
the stellar orbits with mean radii close to the corotation resonance. By
test-particle simulations and different spiral potential models with parameters
constrained on observations, we verified the formation of a minimum with
amplitude ~ 30% - 40% of the background disk stellar density at corotation.
Such minimum is formed by the secular angular momentum transfer between stars
and the spiral density wave on both sides of corotation. We demonstrate that
the secular loss (gain) of angular momentum and decrease (increase) of mean
orbital radius of stars just inside (outside) corotation can counterbalance the
opposite trend of exchange of angular momentum shown by stars orbiting the
librational points L_4/5 at the corotation circle. Such secular processes
actually allow steady spiral waves to promote radial migration across
corotation. We propose some observational evidences for the minimum stellar
density in the Galactic disk, such as its direct relation to the minimum in the
observed rotation curve of the Galaxy at the radius R ~ 9 kpc (for R_0 = 7.5
kpc), as well as its association with a minimum in the distribution of Galactic
radii of a sample of open clusters older than 1 Gyr. The closeness of the solar
orbit radius to the corotation resonance implies that the solar orbit lies
inside a ring of minimum surface density (stellar + gas). This also implies in
a correction to larger values for the estimated total mass of the Galactic
disk, and consequently, a greater contribution of the disk component to the
inner rotation curve of the Galaxy.
