Graphs of Quasicircles and Quasiconformal Homeomorphisms
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Mathematical Dynamics and Fractals
Analytic and geometric function theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 14 January 2026
- Document type
- Preprint