Graphs of Quasicircles and Quasiconformal Homeomorphisms

Katherine Williams Booth; Alexander Nolte; Yvon Verberne

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arXiv · 2601.09892

Graphs of Quasicircles and Quasiconformal Homeomorphisms

Katherine Williams Booth·Alexander Nolte·Yvon Verberne

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Abstract

We give a combinatorial characterization of the group of quasiconformal homeomorphisms of a closed, oriented surface $S$ of genus at least $2$. In particular, we prove they are exactly the automorphisms of a graph of essential quasicircles on $S$ that respect a canonical coarse ordering induced by quality constants. We also discuss the coarse geometry of this graph.

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Katherine Williams Booth, Alexander Nolte, Yvon Verberne. 2026-01-14. Graphs of Quasicircles and Quasiconformal Homeomorphisms. https://arxiv.org/abs/2601.09892

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