Visual metrics on boundaries of hyperbolic spaces
Emily Stark
TL;DR
This paper provides an expository overview of visual metrics on hyperbolic space boundaries, discussing their construction, invariants, and applications, with numerous examples and connections to Gromov's round trees.
Contribution
It offers a comprehensive exposition on visual metrics, quasisymmetries, and invariants in hyperbolic spaces, including new insights and examples from recent research.
Findings
Detailed construction of visual metrics
Analysis of quasisymmetries and invariants
Applications of Gromov's round trees
Abstract
This is an expository article on visual metrics on boundaries of hyperbolic metric spaces. We discuss the construction of visual metrics, quasisymmetries and their invariants, Hausdorff and conformal dimension, and constructions and applications of Gromov's round trees. There is a focus on providing examples throughout. These notes are based on the material of a minicourse given by the author at the 2024 Riverside Workshop in Geometric Group Theory.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Mathematics and Applications