Plane with A∞‐Weighted Metric not Bilipschitz Embeddable to Rn

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Geometric embeddings of metric spaces (2003, unknown): “Read more in [61], [62], [65], [48], [45], [46].”
Assouad's theorem with dimension independent of the snowflaking (2010, background): “[19] T. J. Laakso.”
Fast construction of nets in low dimensional metrics, and their applications (2004, background): “In general, it is impossible to directly apply algorithmic results developed for fixed dimensional Euclidean space to doubling metrics, since there exists doubling metrics that can not embedded in Hilbert space with low distortion of the distances [20].”
Quasisymmetric parametrizations of two-dimensional metric spheres (2001, background): “ with the metric dα((x1,y1),(x2,y2)) = |x1 − x2|+|y1 − y2| α, where 0 < α < 1, will never be quasisymmetrically homeomorphic to S2, see [29, 34]. We also mention that the construction of Laakso [16] provides examples of Ahlfors 2- regular, linearly locally contractible 2-spheres which are not ”