We construct sequences of `expander manifolds' and we use them to show that
there is a complete connected 2-dimensional Riemannian manifold with
discontinuous isoperimetric profile, answering a question of Nardulli and
Pansu. Using expander manifolds in dimension 3 we show that for any $\epsilon ,
M>0$ there is a Riemannian 3-sphere $S$ of volume 1, such that any (not
necessarily connected) surface separating $S$ in two regions of volume greater
than $\epsilon $, has area greater than $M$.