Maps between relatively hyperbolic spaces and between their boundaries

John M Mackay; Alessandro Sisto

doi:https://doi.org/10.1090/tran/9063

Maps between relatively hyperbolic spaces and between their boundaries

John M Mackay^*, Alessandro Sisto

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective) quasi-isometric embeddings between relatively hyperbolic groups/spaces that coarsely respect peripherals, and quasisymmetric embeddings between their boundaries satisfying suitable conditions. Further, we establish a similar correspondence regarding maps with at most polynomial distortion.

Original language	English
Journal	Transactions of the American Mathematical Society
DOIs	https://doi.org/10.1090/tran/9063
Publication status	Published - 19 Oct 2023

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AB - We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective) quasi-isometric embeddings between relatively hyperbolic groups/spaces that coarsely respect peripherals, and quasisymmetric embeddings between their boundaries satisfying suitable conditions. Further, we establish a similar correspondence regarding maps with at most polynomial distortion.

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M3 - Article (Academic Journal)

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JF - Transactions of the American Mathematical Society

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Maps between relatively hyperbolic spaces and between their boundaries

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