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Distortion of quasiconformal maps in terms of the quasihyperbolic metric

Elefterios SoultanisMarshall Williams

subject

Quasiconformal mappingPure mathematicsMathematics::Complex VariablesApplied MathematicsInjective metric space010102 general mathematicsMathematical analysista111Equivalence of metrics01 natural sciencesConvex metric spaceIntrinsic metric010101 applied mathematicsDistortion (mathematics)Metric space0101 mathematicsAnalysisFisher information metricMathematics

description

Abstract We extend a theorem of Gehring and Osgood from 1979–relating to the distortion of the quasihyperbolic metric by a quasiconformal mapping between Euclidean domains–to the setting of metric measure spaces of Q -bounded geometry. When the underlying target space is bounded, we require that the boundary of the image has at least two points. We show that even in the manifold setting, this additional assumption is necessary.

yearjournalcountryeditionlanguage
2013-06-01Journal of mathematical analysis and applications
10.1016/j.jmaa.2013.01.061https://doi.org/10.1016/j.jmaa.2013.01.061