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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.

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Pluripotential theory on Teichmüller space I: Pluricomplex Green function
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by Hideki Miyachi PDF
Conform. Geom. Dyn. 23 (2019), 221-250 Request permission


This is the first paper in a series of investigations of the pluripotential theory on Teichmüller space. One of the main purposes of this paper is to give an alternative approach to the Krushkal formula of the pluricomplex Green function on Teichmüller space. We also show that Teichmüller space carries a natural stratified structure of real-analytic submanifolds defined from the structure of singularities of the initial differentials of the Teichmüller mappings from a given point. We will also give a description of the Levi form of the pluricomplex Green function using the Thurston symplectic form via Dumas’ symplectic structure on the space of holomorphic quadratic differentials.
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Additional Information
  • Hideki Miyachi
  • Affiliation: Division of Mathematical and Physical Sciences, Graduate School of Natural Science & Technology, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa, 920-1192, Japan
  • MR Author ID: 650573
  • ORCID: 0000-0003-4318-9539
  • Email:
  • Received by editor(s): January 14, 2019
  • Published electronically: November 7, 2019
  • Additional Notes: This work was partially supported by JSPS KAKENHI Grant Numbers 16K05202, 16H03933, 17H02843
  • © Copyright 2019 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 23 (2019), 221-250
  • MSC (2010): Primary 30F60, 32G15, 57M50, 31B05, 32U05, 32U35
  • DOI:
  • MathSciNet review: 4028456