Quasisymmetric embeddability of weak tangents

Wenbo Li
2021 Annales Fennici Mathematici  
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
more » ... bility 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.
doi:10.5186/aasfm.2021.4656 fatcat:y7372oiedvez5fve32lpybae4m