Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Convergence of Teichmüller deformations in the universal Teichmüller space
HTML articles powered by AMS MathViewer

by Hideki Miyachi and Dragomir Šarić PDF
Proc. Amer. Math. Soc. 147 (2019), 4877-4889 Request permission

Abstract:

Let $\varphi :\mathbb {D}\to \mathbb {C}$ be an integrable holomorphic function on the unit disk $\mathbb {D}$ and let $D_{\varphi }:\mathbb {D}\to T(\mathbb {D})$ be the corresponding Teichmüller disk in the universal Teichmüller space $T(\mathbb {D})$. For a positive $t$ it is known that $D_{\varphi }(t)\to [\mu _{\varphi }]\in PML_b(\mathbb {D})$ as $t\to 1$, where $\mu _{\varphi }$ is a bounded measured lamination representing a point on the Thurston boundary of $T(\mathbb {D})$. We extend this result by showing that $D_{\varphi }\colon \mathbb {D}\to T(\mathbb {D})$ extends as a continuous map from the closed disk $\overline {\mathbb {D}}$ to the Thurston bordification. In addition, we prove that the rate of convergence of $D_{\varphi }(\lambda )$ when $\lambda \to e^{i\theta }$ is independent of the type of the approach to $e^{i\theta }\in \partial \mathbb {D}$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 30F60, 30C62, 30L99
  • Retrieve articles in all journals with MSC (2010): 30F60, 30C62, 30L99
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
  • MR Author ID: 650573
  • ORCID: 0000-0003-4318-9539
  • Email: miyachi@se.kanazawa-u.ac.jp
  • Dragomir Šarić
  • Affiliation: Department of Mathematics, Queens College of CUNY, 65-30 Kissena Boulevard, Flushing, New York 11367; and Mathematics Ph.D. Program, The CUNY Graduate Center, 365 Fifth Avenue, New York, New York 10016-4309
  • Email: Dragomir.Saric@qc.cuny.edu
  • Received by editor(s): October 3, 2018
  • Received by editor(s) in revised form: February 19, 2019
  • Published electronically: May 17, 2019
  • Additional Notes: The first author was partially supported by JSPS KAKENHI Grant Numbers 16K05202, 16H03933, 17H02843.
    The second author was partially supported by a Simons Foundation grant, Grant Number 346391.
  • Communicated by: Ken Bromberg
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4877-4889
  • MSC (2010): Primary 30F60; Secondary 30C62, 30L99
  • DOI: https://doi.org/10.1090/proc/14598
  • MathSciNet review: 4011520