  A question whether sufficiently regular manifold automorphisms may have
wandering domains with controlled geometry is answered in the negative for
quasiconformal or smooth homeomorphisms of $n$-tori, $n\ge2$, and hyperbolic
surfaces. Besides control on geometry of wandering domains, the assumptions are
either analytic, e.g., minimal sets having measure zero or supporting invariant
conformal structures, or geometric, such as uniform relative separation of
wandering domains.
