ABSTRACT
In this chapter we study isoperimetric inequalities for combable groups in dimension greater than two. The existence of such inequalities is due to Thurston, and the proofs presented here were worked out by Epstein. In Section 10.1 we set up combinatorial constructs that make it easier to carry out the proofs. Section 10.2 presents the inequalities proper. Section 10.3 extends the inequalities to more general chains, using a standard method from geometric measure theory, originally due to Federer and Fleming in [FF60]. Thanks are due to Brian White who explained this method to Epstein.
