6533b825fe1ef96bd12826e5
RESEARCH PRODUCT
Exceptional Sets for Quasiconformal Mappings in General Metric Spaces
Pekka KoskelaKevin Wildricksubject
Pure mathematicsQuasiconformal mappingMathematics::Complex VariablesGeneral MathematicsInjective metric spaceMathematical analysisPoincaré inequalityIntrinsic metricConvex metric spacesymbols.namesakeMetric spaceHausdorff distancesymbolsHausdorff measureMathematicsdescription
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.
year | journal | country | edition | language |
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2008-01-01 | International Mathematics Research Notices |