Quasiconformal and geodesic trees

Mario Bonk, Daniel Meyer Fundamenta Mathematicae MSC: Primary 30L10; Secondary 51F99. DOI: 10.4064/fm749-7-2019 Published online: 24 February 2020


A quasiconformal tree is a metric tree that is doubling and of bounded turning. We prove that every quasiconformal tree is quasisymmetrically equivalent to a geodesic tree with Hausdorff dimension arbitrarily close to 1.


  • Mario BonkDepartment of Mathematics
    University of California
    Los Angeles, CA 90095, U.S.A.
  • Daniel MeyerDepartment of Mathematical Sciences
    University of Liverpool
    Liverpool L69 7ZL, United Kingdom

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