Skip to Main Content

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.


Conformal Grushin spaces
HTML articles powered by AMS MathViewer

by Matthew Romney
Conform. Geom. Dyn. 20 (2016), 97-115
Published electronically: May 2, 2016


We introduce a class of metrics on $\mathbb {R}^n$ generalizing the classical Grushin plane. These are length metrics defined by the line element $ds = d_E(\cdot ,Y)^{-\beta }ds_E$ for a closed nonempty subset $Y \subset \mathbb {R}^n$ and $\beta \in [0,1)$. We prove, assuming a Hölder condition on the metric, that these spaces are quasisymmetrically equivalent to $\mathbb {R}^n$ and can be embedded in some larger Euclidean space under a bi-Lipschitz map. Our main tool is an embedding characterization due to Seo, which we strengthen by removing the hypothesis of uniform perfectness. In the two-dimensional case, we give another proof of bi-Lipschitz embeddability based on growth bounds on sectional curvature.
Similar Articles
  • Retrieve articles in Conformal Geometry and Dynamics of the American Mathematical Society with MSC (2010): 30L05
  • Retrieve articles in all journals with MSC (2010): 30L05
Bibliographic Information
  • Matthew Romney
  • Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green St., Urbana, Illinois 61801
  • MR Author ID: 1021342
  • Email:
  • Received by editor(s): October 28, 2015
  • Received by editor(s) in revised form: January 26, 2016, and February 15, 2016
  • Published electronically: May 2, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 20 (2016), 97-115
  • MSC (2010): Primary 30L05
  • DOI:
  • MathSciNet review: 3492624