On the conformal dimension of product measures

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http://hdl.handle.net/10138/307141

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Bate , D & Orponen , T 2018 , ' On the conformal dimension of product measures ' , Proceedings of the London Mathematical Society , vol. 117 , no. 2 , pp. 277-302 . https://doi.org/10.1112/plms.12130

Title: On the conformal dimension of product measures
Author: Bate, David; Orponen, Tuomas
Contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2018-08
Language: eng
Number of pages: 26
Belongs to series: Proceedings of the London Mathematical Society
ISSN: 0024-6115
URI: http://hdl.handle.net/10138/307141
Abstract: Given a compact set E. Rd-1, d >= 1, write KE := [0, 1] x 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 dim(H) f(K-E) >= dim(H) K-E. We prove that the measure-theoretic analogue of the result is not true. For any d >= 2 and 0 0, there exists a quasisymmetric embedding F : KE. Rd such that dimH F-v
Subject: SETS
HAUSDORFF
111 Mathematics
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