Filling in solvable groups and in lattices in semisimple groups

We prove that the filling order is quadratic for a large class of solvable groups and asymptotically quadratic for all <f>Q</f>-rank one lattices in semisimple groups of <f>R</f>-rank at least <f>3</f>. As a byproduct of auxiliary results we give a shorter proof of the theorem on the nondistorsion of horospheres providing also an estimate of a nondistorsion constant. [Copyright &y& Elsevier]