Conformal dimension and its attainment on self-similar Laakso-type fractal spaces
A general construction of Laakso-type fractal spaces was recently introduced by the first two authors. In this paper, we establish a simple condition characterizing when the Ahlfors regular conformal dimension of a symmetric Laakso-type fractal space is attained. The attaining metrics are constructed explicitly. This gives new examples of attainment and clarifies the possible obstructions.
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