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Conformal Geometry and Dynamics

Published by the American Mathematical Society since 1997, the purpose of this electronic-only journal is to provide a forum for mathematical work in related fields broadly described as conformal geometry and dynamics. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.49.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Maps on the Morse boundary
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by Qing Liu
Conform. Geom. Dyn. 26 (2022), 67-96
Published electronically: August 11, 2022


For a proper geodesic metric space, the Morse boundary focuses on the hyperbolic-like directions in the space. The Morse boundary is a quasi-isometry invariant. That is, a quasi-isometry between two spaces induces a homeomorphism on their Morse boundaries. In this paper, we investigate additional structures on the Morse boundary which determine the space up to a quasi-isometry. We prove that a homeomorphism between the Morse boundaries of two proper, cocompact spaces is induced by a quasi-isometry if and only if both the homeomorphism and its inverse are bihölder, or quasi-symmetric, or strongly quasi-conformal.
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Bibliographic Information
  • Qing Liu
  • Affiliation: School of Mathematical Sciences & LPMC, Nankai University, Tianjin 300071, People’s Republic of China
  • ORCID: 0000-0002-2216-8029
  • Email:
  • Received by editor(s): May 2, 2020
  • Received by editor(s) in revised form: March 2, 2022, and May 22, 2022
  • Published electronically: August 11, 2022
  • Additional Notes: This work was supported by the Fundamental Research Funds for the Central Universities, Nankai University (grant no. 63221034).
  • © Copyright 2022 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 26 (2022), 67-96
  • MSC (2020): Primary 20F65, 57M07
  • DOI:
  • MathSciNet review: 4467305