Carath\'eodory metric on some generalized Teichm\"uller spaces
Xinlong Dong, Sudeb Mitra
TL;DR
This paper investigates the completeness of the Carathéodory metric on various generalized Teichmüller spaces, extending known results to product spaces and spaces of closed sets in the Riemann sphere.
Contribution
It extends the understanding of the Carathéodory metric's completeness to new classes of generalized Teichmüller spaces, including product spaces and spaces of closed sets.
Findings
Completeness of the Carathéodory metric on product Teichmüller spaces.
Completeness of the Carathéodory metric on Teichmüller space of a closed set.
Extension of Earle and Miyachi's results to broader contexts.
Abstract
We study the Carath\'eodory metric on some generalized Teichm\"uller spaces. Earle showed that the Carath\'eodory metric is complete on any Teichm\"uller space. Miyachi extended this result for Asymptotic Teichm\"uller spaces. We study the completeness of the Carath\'eodory metric on product Teichm\"uller spaces and on the Teichm\"uller space of a closed set in the Riemann sphere.
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Taxonomy
TopicsAnalytic and geometric function theory · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems