6533b861fe1ef96bd12c5082

RESEARCH PRODUCT

Quasispheres and metric doubling measures

Martti RasimusAtte LohvansuuKai Rajala

subject

Pure mathematicsmetric spaces30L10 (Primary) 30C65 28A75 (Secondary)General MathematicsMathematicsofComputing_GENERALCharacterization (mathematics)01 natural sciencesMeasure (mathematics)Intrinsic metricfunktioteoria0103 physical sciencesFOS: MathematicsComplex Variables (math.CV)0101 mathematicsMathematicsDiscrete mathematicsMathematics - Complex VariablesApplied MathematicsInjective metric spaceta111010102 general mathematicsmetriset avaruudetcomplex analysisConvex metric spacemeasure theoryMetric (mathematics)mittateoria010307 mathematical physicsFisher information metric

description

Applying the Bonk-Kleiner characterization of Ahlfors 2-regular quasispheres, we show that a metric two-sphere $X$ is a quasisphere if and only if $X$ is linearly locally connected and carries a weak metric doubling measure, i.e., a measure that deforms the metric on $X$ without much shrinking.

yearjournalcountryeditionlanguage
2018-01-01Proceedings of the American Mathematical Society
https://doi.org/10.1090/proc/13971