6533b863fe1ef96bd12c78c2

RESEARCH PRODUCT

Nonexistence of Quasiconformal Maps Between Certain Metric Measure Spaces

Pekka KoskelaKatrin FässlerEnrico Le Donne

subject

Mathematics - Differential Geometrymetric measure spacesPure mathematicsMathematics::Dynamical SystemsMathematics::Complex VariablesGeneral MathematicsExistential quantificationta111010102 general mathematicsMetric Geometry (math.MG)01 natural sciencesMeasure (mathematics)quasiconformal equivalenceDifferential Geometry (math.DG)Mathematics - Metric Geometryquasiconformal mappingsMathematics - Classical Analysis and ODEs0103 physical sciencesMetric (mathematics)Classical Analysis and ODEs (math.CA)FOS: MathematicsMathematics (all)010307 mathematical physics0101 mathematicsMathematics

description

We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application, we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.

yearjournalcountryeditionlanguage
2013-12-04International Mathematics Research Notices
https://doi.org/10.1093/imrn/rnu153