Connected components of closed affine Deligne-Lusztig varieties
  We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. Especially, we show that such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. From the dimension formula for affine Deligne-Lusztig varieties we obtain a description of the set of these varieties that are zero-dimensional. 
Eva Viehmann