Geodesic
Quasisymmetric embeddability of weak tangents
Wenbo Li1
1 University of Toronto, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 909-944.

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In this paper, we study the quasisymmetric embeddability of weak tangents of metric spaces. We first show that quasisymmetric embeddability is hereditary, i.e., if $X$ can be quasisymmetrically embedded into $Y$, then every weak tangent of $X$ can be quasisymmetrically embedded into some weak tangent of $Y$, given that $X$ is proper and doubling. However, the converse is not true in general; we will illustrate this with several counterexamples. In special situations, we are able to show that the embeddability of weak tangents implies global or local embeddability of the ambient space. Finally, we apply our results to Gromov hyperbolic groups and visual spheres of expanding Thurston maps.
Keywords: Weak tangents, quasisymmetric embeddings, hyperbolic spaces, expanding Thurston maps

Wenbo Li 1

1 University of Toronto, Department of Mathematics 
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Wenbo Li. Quasisymmetric embeddability of weak tangents. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 909-944. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a18/