  We show how the infinite color-Coulomb energy of color-charged states is
related to enhanced density of near-zero modes of the Faddeev-Popov operator,
and calculate this density numerically for both pure Yang-Mills and gauge-Higgs
systems at zero temperature, and for pure gauge theory in the deconfined phase.
We find that the enhancement of the eigenvalue density is tied to the presence
of percolating center vortex configurations, and that this property disappears
when center vortices are either removed from the lattice configurations, or
cease to percolate. We further demonstrate that thin center vortices have a
special geometrical status in gauge-field configuration space: Thin vortices
are located at conical or wedge singularities on the Gribov horizon. We show
that the Gribov region is itself a convex manifold in lattice configuration
space. The Coulomb gauge condition also has a special status; it is shown to be
an attractive fixed point of a more general gauge condition, interpolating
between the Coulomb and Landau gauges.
