Conformal assouad dimension and modulus

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On the Assouad dimension of self-similar sets with overlaps (2014, background): “Here the conformal dimension of X is the infimum of the dimension of quasi-conformal images of X. Keith and Laakso [15] study Ahlfors regular metric spaces whose Assouad dimension cannot be lowered by quasi-conformal maps and Bonk and Kleiner [4] apply this work to resolve Cannon’s conjecture in cer”
Assouad dimension of self-affine carpets (2010, background): “Calculating the conformal dimension (Assouad or Hausdorff) of a self-similar carpet is a challenging open problem (see, for example, [8]).”
Geometric embeddings of metric spaces (2003, unknown): “Read more in [26], [52], [42], [23], [41].”
Assouad Dimension and Fractal Geometry (2020, methodology): “One of the most effective ways to bound the Assouad dimension of a set from below is to use weak tangents; an approach pioneered by Mackay and Tyson [195] with ideas going back to Keith and Laakso [164].”
Conformal dimension and Gromov hyperbolic groups with 2-sphere boundary (2002, background): “We remark that it follows from [14] that the conformal dimension of S is less than its Hausdorff dimension.”
The Poincare inequality is an open ended condition (2008, background): “Laakso and the first author ([30]) demonstrated that complete Ahlfors α-regular metric measure spaces, α > 1, cannot have their Assouad dimension lowered through quasisymmetric mappings if and only if they possess at least one weak-tangent”