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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.


The realization problem for Jørgensen numbers
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by Yasushi Yamashita and Ryosuke Yamazaki
Conform. Geom. Dyn. 23 (2019), 17-31
Published electronically: February 25, 2019


Let $G$ be a two-generator subgroup of $\mathrm {PSL}(2, \mathbb {C})$. The Jørgensen number $J(G)$ of $G$ is defined by \[ J(G) = \inf \{ |\mathrm {tr}^2 A-4| + |\mathrm {tr} [A,B]-2| \: ; \: G=\langle A, B\rangle \}. \] If $G$ is a non-elementary Kleinian group, then $J(G)\geq 1$. This inequality is called Jørgensen’s inequality. In this paper, we show that, for any $r\geq 1$, there exists a non-elementary Kleinian group whose Jørgensen number is equal to $r$. This answers a question posed by Oichi and Sato. We also present our computer generated picture which estimates Jørgensen numbers from above in the diagonal slice of Schottky space.
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Bibliographic Information
  • Yasushi Yamashita
  • Affiliation: Nara Women’s University, Kitauoyanishi-machi, Nara-shi, Nara 630-8506, Japan
  • MR Author ID: 310816
  • Email:
  • Ryosuke Yamazaki
  • Affiliation: Gakushuin Boys’ Senior High School, 1-5-1 Mejiro, Toshima-ku, Tokyo 171-0031, Japan
  • Email:
  • Received by editor(s): August 21, 2017
  • Received by editor(s) in revised form: April 15, 2018, and September 26, 2018
  • Published electronically: February 25, 2019
  • Additional Notes: This work was supported by JSPS KAKENHI Grant Number 26400088.
  • © Copyright 2019 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 23 (2019), 17-31
  • MSC (2010): Primary 30F40, 57M50
  • DOI:
  • MathSciNet review: 3916474