Geodesic
Carathéodory metric on some generalized Teichmüller spaces
Xinlong Dong1 ; Sudeb Mitra2
1 City University of New York, Kingsborough Community College, Department of Mathematics and Computer Science
2 Queens College of the City University of New York, Department of Mathematics, and Graduate Center of the City University of New York, Department of Mathematics
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 797-807.

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We study the Carathéodory metric on some generalized Teichmüller spaces. Our paper is especially inspired by the papers by Earle (1974) and Miyachi (2006). Earle (1974) showed that the Carathéodory metric is complete on any Teichmüller space. Miyachi (2006) extended this result for asymptotic Teichmüller spaces. We study the completeness of the Carathéodory metric on product Teichmüller spaces and on the Teichmüller space of a closed set in the Riemann sphere.
DOI : 10.54330/afm.141665
Keywords: Teichmüller spaces, Carathéodory metric, Kobayashi metric

Xinlong Dong 1 ; Sudeb Mitra 2

1 City University of New York, Kingsborough Community College, Department of Mathematics and Computer Science
2 Queens College of the City University of New York, Department of Mathematics, and Graduate Center of the City University of New York, Department of Mathematics 
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Xinlong Dong; Sudeb Mitra. Carathéodory metric on some generalized Teichmüller spaces. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 797-807. doi : 10.54330/afm.141665. http://geodesic.mathdoc.fr/articles/10.54330/afm.141665/

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