  Complete gauge-fixing beyond perturbation theory in non-Abelian gauge
theories is a non-trivial problem. This is particularly evident in covariant
gauges, where the Gribov-Singer ambiguity gives an explicit formulation of the
problem. In practice, this is a problem if gauge-dependent quantities between
different methods, especially lattice and continuum methods, should be
compared: Only when treating the Gribov-Singer ambiguity in the same way is the
comparison meaningful. To provide a better basis for such a comparison the
structure of the first Gribov region in Landau gauge, a subset of all possible
gauge copies satisfying the perturbative Landau gauge condition, will be
investigated. To this end, lattice gauge theory will be used to investigate a
two-dimensional projection of the region for SU(2) Yang-Mills theory in two,
three, and four dimensions for a wide range of volumes and discretizations.
