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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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.


Cusps in complex boundaries of one-dimensional Teichmüller space
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by Hideki Miyachi PDF
Conform. Geom. Dyn. 7 (2003), 103-151 Request permission


This paper gives a concrete proof of the conjectural phenomena on the complex boundary one-dimensional slices: every rational boundary point is cusp shaped. This paper treats this problem for Bers slices, the Earle slice, and the Maskit slice. In proving this, we also show that every Teichmüller modular transformation acting on a Bers slice can be extended as a quasi-conformal mapping on its ambient space. Furthermore, using this extension, we discuss similarity phenomena on the boundaries of Bers slices, and also compare these phenomena with results in complex dynamics. We will also give a result, related to the theory of L. Keen and C. Series, of pleated varieties in quasifuchsian space of once punctured tori.
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Additional Information
  • Hideki Miyachi
  • Affiliation: Department of Mathematics, Osaka City University, Sumiyoshi, Osaka, 558-8585, Japan
  • Address at time of publication: Graduate School of Science, Department of Mathematics, Osaka University, 1-1, Machikaneyama-cho, Toyonaka, Osaka, 560-0023, Japan
  • MR Author ID: 650573
  • Email:,
  • Received by editor(s): July 2, 2000
  • Received by editor(s) in revised form: February 20, 2003
  • Published electronically: September 9, 2003
  • Additional Notes: This work was done when the author was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

  • Dedicated: Dedicated to my father Kenji Miyachi for his 60th Birthday
  • © Copyright 2003 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 7 (2003), 103-151
  • MSC (2000): Primary 30F40, 30F60; Secondary 37F30, 37F45
  • DOI:
  • MathSciNet review: 2023050