6533b835fe1ef96bd129f67c

RESEARCH PRODUCT

Rigidity of quasisymmetric mappings on self-affine carpets

Eino RossiAntti KäenmäkiTuomo Ojala

subject

Class (set theory)Pure mathematicsMathematics::Dynamical SystemsGeneral Mathematicsquasisymmetric mapsMathematics::General TopologyPhysics::OpticsConformal mapRigidity (psychology)01 natural sciencesDimension (vector space)0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric Geometry0101 mathematicsself-affine carpetsMathematicsta111010102 general mathematicsPhysics::Classical PhysicsMathematics - Classical Analysis and ODEs010307 mathematical physicsAffine transformation28A80 37F35 30C62 30L10

description

We show that the class of quasisymmetric maps between horizontal self-affine carpets is rigid. Such maps can only exist when the dimensions of the carpets coincide, and in this case, the quasisymmetric maps are quasi-Lipschitz. We also show that horizontal self-affine carpets are minimal for the conformal Assouad dimension.

yearjournalcountryeditionlanguage
2016-07-08
10.1093/imrn/rnw336http://arxiv.org/abs/1607.02244