  We bound the higher-order Dehn functions and other filling invariants of
certain Carnot groups using approximation techniques. These groups include the
higher-dimensional Heisenberg groups, jet groups, and central products of
two-step nilpotent groups. Some consequences of this work are a construction of
groups with arbitrarily large nilpotency class that have euclidean
n-dimensional filling volume functions, and a proof of part of a conjecture of
Gromov on the higher-order filling functions of the higher-dimensional
Heisenberg groups.
