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DOI: 10.5186/aasfm.2021.4656

Quasisymmetric Embeddability of Weak Tangents

Wen-Bo Li
Dec 2018
摘要
In this paper, we study the quasisymmetric embeddability of weak tangents ofmetric spaces. We first show that quasisymmetric embeddability is hereditary,i.e., if $X$ can be quasisymmetrically embedded into $Y$, then every weaktangent of $X$ can be quasisymmetrically embedded into some weak tangent of$Y$, given that $X$ is proper and doubling. However, the converse is not truein general; we will illustrate this with several counterexamples. In specialsituations, we are able to show that the embeddability of weak tangents impliesglobal or local embeddability of the ambient space. Finally, we apply ourresults to Gromov hyperbolic groups and visual spheres of expanding Thurstonmaps.
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