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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.


Completeness of $p$ -Weil-Petersson distance
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by Masahiro Yanagishita
Conform. Geom. Dyn. 26 (2022), 34-45
Published electronically: May 10, 2022


Our goal of this paper is to research the completeness of the $p$ -Weil-Petersson distance, which is induced by the $p$ -Weil-Petersson metric on the $p$ -integrable Teichmüller space of hyperbolic Riemann surfaces. As a result, we see that the metric is incomplete for all the hyperbolic Riemann surfaces with Lehner’s condition except for the ones that are conformally equivalent to either the unit disk or the punctured unit disk. The proof is based on the one by Wolpert’s original paper, which is given in the case of compact Riemann surfaces.
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Bibliographic Information
  • Masahiro Yanagishita
  • Affiliation: Department of Applied Science, Graduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Ube-shi, Yamaguchi 755-8611, Japan
  • MR Author ID: 1029821
  • ORCID: 0000-0002-5444-3507
  • Email:
  • Received by editor(s): March 1, 2021
  • Received by editor(s) in revised form: January 24, 2022
  • Published electronically: May 10, 2022
  • Additional Notes: This work was supported by JSPS KAKENHI 18K13410
  • © Copyright 2022 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 26 (2022), 34-45
  • MSC (2020): Primary 30F60; Secondary 32G15, 30C62
  • DOI:
  • MathSciNet review: 4419576