No bounded geometry wandering domains for sufficiently regular automorphisms

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 n -tori, n ≥ 2 n 2, 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.