Carathéodory metric on some generalized Teichmüller spaces

Authors

  • Xinlong Dong City University of New York, Kingsborough Community College, Department of Mathematics and Computer Science
  • Sudeb Mitra 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

DOI:

https://doi.org/10.54330/afm.141665

Keywords:

Teichmüller spaces, Carathéodory metric, Kobayashi metric

Abstract

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.

Downloads

Published

2023-12-01

Issue

Vol. 48 No. 2 (2023)

Section

Articles

License

Copyright (c) 2023 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Dong, X., & Mitra, S. (2023). Carathéodory metric on some generalized Teichmüller spaces. Annales Fennici Mathematici, 48(2), 797-807. https://doi.org/10.54330/afm.141665