Quasiconformal mappings that highly distort dimensions of many parallel   lines
  We construct a quasiconformal mapping of $n$-dimensional Euclidean space, $n \geq 2$, that simultaneously distorts the Hausdorff dimension of a nearly maximal collection of parallel lines by a given amount. This answers a question of Balogh, Monti, and Tyson. 
Zolt\'an M. Balogh, Jeremy T. Tyson, Kevin Wildrick
math.MG