Asymptotic Behavior of Cosmologies with $\Lambda >0$ in 2+1 Dimensions
  We study, using Mean Curvature Flow methods, 2+1 dimensional cosmologies with
a positive cosmological constant and matter satisfying the dominant and the
strong energy conditions. If the spatial slices are compact with non-positive
Euler characteristic and are initially expanding everywhere, then we prove that
the spatial slices reach infinite volume, asymptotically converge on average to
de Sitter and they become, almost everywhere, physically indistinguishable from
de Sitter. This holds true notwithstanding the presence of initial
arbitrarily-large density fluctuations and the formation of black holes.
