The Sheet of Giants: Unusual Properties of the Milky Way's Immediate
  Neighbourhood
  We quantify the shape and overdensity of the galaxy distribution in the
`Local Sheet' within a sphere of $R=8$ Mpc, and compare these properties with
the expectations of the $\Lambda$CDM model. We measure ellipsoidal axis ratios
of $c/a\approx0.16$ and $b/a\approx0.79$, indicating that the distribution of
galaxies in the Local Volume can be approximated by a flattened oblate
ellipsoid, consistent with the `sheet'-like configuration noted in previous
studies. In contrast with previous estimates that the Local Sheet has a density
close to average, we find that the number density of faint and bright galaxies
in the Local Volume is $\approx1.7$ and $\approx5.2$ times denser,
respectively, than the mean number density of galaxies of the same luminosity.
Comparison with simulations shows that the number density contrasts of bright
and faint galaxies within $8$ Mpc alone make the Local Volume a $\approx
2.5\sigma$ outlier in the $\Lambda$CDM cosmology. Our results indicate that the
cosmic neighbourhood of the Milky Way may be unusual for galaxies of similar
luminosity. The impact of the peculiar properties of our neighbourhood on the
properties of the Milky Way and other nearby galaxies is not yet understood and
warrants further study.
