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Conformal Geometry and Dynamics

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Bilipschitz equivalence of trees and hyperbolic fillings


Author: Jeff Lindquist
Journal: Conform. Geom. Dyn. 22 (2018), 225-234
MSC (2010): Primary 30C65; Secondary 52C99, 05C63
DOI: https://doi.org/10.1090/ecgd/322
Published electronically: September 24, 2018
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Abstract: We show that quasi-isometries between uniformly discrete bounded geometry spaces that satisfy linear isoperimetric inequalities are within bounded distance to bilipschitz equivalences. We apply this result to regularly branching trees and hyperbolic fillings of compact, Ahlfors regular metric spaces.


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Additional Information

Jeff Lindquist
Affiliation: PL 68 (Gustaf Hällströmin katu 2b) 00014 Helsingin Yliopisto
Address at time of publication: University of Cincinnati, 2815 Commons Way, Cincinnati, Ohio 45221
Email: Lindqujy@ucmail.uc.edu.

DOI: https://doi.org/10.1090/ecgd/322
Received by editor(s): August 3, 2017
Received by editor(s) in revised form: September 3, 2017, February 7, 2018, and June 26, 2018
Published electronically: September 24, 2018
Additional Notes: At the University of Helsinki, the author was supported by Academy of Finland grants 297258 and 308759. At the University of California, Los Angeles, the author was partially supported by NSF grants DMS-1506099 and DMS-1162471.
This work was based on work from the author’s thesis.
Article copyright: © Copyright 2018 American Mathematical Society

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