Uniformization of quasitrees

Daniel Meyer
University of Liverpool

A quasisymmetry maps balls in a controlled manner. These maps are generalizations of conformal maps and may be viewed as a global versions of quasiconformal maps. Originally, they were introduced in the context of geometric function theory, but appear now in geometric group theory and analysis on metric spaces among others. The quasisymmetric uniformization problem asks when a given metric space is quasisymmetric to some model space. Here we consider ``quasitrees''. We show that any such tree is quasisymmetrically equivalent to a geodesic tree. Under additional assumptions it is quasisymmetric to the ``continuum self-similar tree''. This is joint work with Mario Bonk.

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