Quasiconformal and geodesic trees
Mario Bonk, Daniel Meyer
Abstract
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.
Topics & Concepts
MathematicsTree (set theory)GeodesicBounded functionQuasiconformal mappingMetric (unit)Hausdorff dimensionDimension (graph theory)Pure mathematicsHausdorff measureCombinatoricsHausdorff distanceMinkowski–Bouligand dimensionMetric spaceHausdorff spaceDiscrete mathematicsMathematical analysisGeometric and Algebraic TopologyQuasicrystal Structures and PropertiesMathematical Dynamics and Fractals