Quasisymmetric embeddability of weak tangents

Authors

  • Wenbo Li University of Toronto, Department of Mathematics

Keywords:

Weak tangents, quasisymmetric embeddings, hyperbolic spaces, expanding Thurston maps

Abstract

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.
Section
Articles

Published

2021-08-18

How to Cite

Li, W. (2021). Quasisymmetric embeddability of weak tangents. Annales Fennici Mathematici, 46(2), 909–944. Retrieved from https://afm.journal.fi/article/view/110886