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Pluripotential theory on Teichmüller space I: Pluricomplex Green function


Author: Hideki Miyachi
Journal: Conform. Geom. Dyn. 23 (2019), 221-250
MSC (2010): Primary 30F60, 32G15, 57M50, 31B05, 32U05, 32U35
DOI: https://doi.org/10.1090/ecgd/340
Published electronically: November 7, 2019
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Abstract: 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
Email: miyachi@se.kanazawa-u.ac.jp

DOI: https://doi.org/10.1090/ecgd/340
Keywords: Singular Euclidean structures, Teichm{\"u}ller space, Teichm{\"u}ller distance, Levi forms, pluricomplex Green functions
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
Article copyright: © Copyright 2019 American Mathematical Society