Coarse differentiation and quasi-isometries of a class of solvable Lie groups I

Abstract

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.

48 pages (10pt, wide textwidth), 8 figures