  The main results in this paper provide upper bounds of the second order Dehn
functions for three-dimensional groups Nil and Sol. These upper bounds are
obtained by using the Varopoulos transport argument on dual graphs. The first
step is to start with reduced handlebody diagrams of the three-dimensional
balls either immersed or embedded in the universal covers of each group and
then define dual graphs using the 0-handles as vertices, 1-handles as edges.
The idea is to reduce the original isoperimetric problem involving volume of
three-dimensional balls and areas of their boundary spheres to a problem
involving Varopoulos' notion of volume and boundary of finite domains in dual
graphs.
