0000000000049516

AUTHOR

Marshall Williams

showing 2 related works from this author

The branch set of a quasiregular mapping between metric manifolds

2016

Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.

Discrete mathematicsConjectureMathematics::Complex VariablesOpen problem010102 general mathematicsMathematical analysisGeneral Medicine01 natural sciences010101 applied mathematicsSet (abstract data type)Metric spaceMetric (mathematics)Mathematics::Metric GeometryCountable set0101 mathematicsMathematicsComptes Rendus Mathematique
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Distortion of quasiconformal maps in terms of the quasihyperbolic metric

2013

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.

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 metricMathematicsJournal of mathematical analysis and applications
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