No bounded geometry wandering domains for sufficiently regular automorphisms

Sergei Merenkov

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arXiv · 2105.08760

No bounded geometry wandering domains for sufficiently regular automorphisms

Sergei Merenkov

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Abstract

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.

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Sergei Merenkov. 2022-05-23. No bounded geometry wandering domains for sufficiently regular automorphisms. https://arxiv.org/abs/2105.08760

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