Coarse differentiation and quasi-isometries of a class of solvable Lie   groups I
  This is the first of two papers which aim to understand quasi-isometries of a subclass of unimodular split solvable Lie groups. In the present paper, we show that locally (in a coarse sense), a quasi-isometry between two groups in this subclass is close to a map that respects their group structures. 
Irine Peng