On the Carathéodory metric of universal Teichmüller space-Reference-Cited by-同舟云学术

On the Carathéodory metric of universal Teichmüller space

Published:2022-01-28 Issue:1 Volume:19 Page:75-87
ISSN:1810-3200
Container-title:Ukrainian Mathematical Bulletin
language:uk
Short-container-title:UMB

Author:

Krushkal Samuel¹

Affiliation:

1. Department of Mathematics, Bar-Ilan University, Israel, Department of Mathematics, University of Virginia, Charlottesville, USA

Abstract

In contrast to finite dimensional Teichmuller spaces, all non-expanding invariant metrics on the universal Teichmuller space coincide. This important fact found various applications. We give its new, simplified proof based on some deep features of the Grunsky operator, which intrinsically relate to the universal Teichmuller space. This approach also yields a quantitative answer to Ahlfors' question.

Publisher

Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine

Reference21 articles.

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