We give conditions under which a quasi-isometric map between direct products of hyperbolic spaces splits as a direct product up to bounded distance and permutation of factors. This is a variation on a result due to Kapovich, Kleiner and Leeb.
Preprint, Warwick, April 2014.
Revised, March 2016.
Internat. J. Algebra Comput. 26 (2016) 619-633.