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RESEARCH PRODUCT

Exceptional Sets for Quasiconformal Mappings in General Metric Spaces

Pekka KoskelaKevin Wildrick

subject

Pure mathematicsQuasiconformal mappingMathematics::Complex VariablesGeneral MathematicsInjective metric spaceMathematical analysisPoincaré inequalityIntrinsic metricConvex metric spacesymbols.namesakeMetric spaceHausdorff distancesymbolsHausdorff measureMathematics

description

A theorem of Balogh, Koskela, and Rogovin states that in Ahlfors Q-regular metric spaces which support a p-Poincare inequality, , an exceptional set of -finite (Q−p)- dimensional Hausdorff measure can be taken in the definition of a quasiconformal mapping while retaining Sobolev regularity analogous to that of the Euclidean setting. Through examples, we show that the assumption of a Poincare inequality cannot be removed.

https://doi.org/10.1093/imrn/rnn020