On the conformal dimension of product measures

@article{Bate2017OnTC,
  title={On the conformal dimension of product measures},
  author={David Bate and Tuomas Orponen},
  journal={Proceedings of the London Mathematical Society},
  year={2017},
  volume={117}
}
Given a compact set E⊂Rd−1 , d⩾1 , write KE:=[0,1]×E⊂Rd . A theorem of Bishop and Tyson states that any set of the form KE is minimal for conformal dimension: If (X,d) is a metric space and f:KE→(X,d) is a quasisymmetric homeomorphism, then dimHf(KE)⩾dimHKE.We prove that the measure‐theoretic analogue of the result is not true. For any d⩾2 and 0⩽s0 , there exists a quasisymmetric embedding F:KE→Rd such that dimHF♯ν 

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