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Uniformly Bounded Maximal ϕ-Disks, Bers Space and Harmonic Maps

Anić, I. and Marković, V. and Mateljević, M. (2000) Uniformly Bounded Maximal ϕ-Disks, Bers Space and Harmonic Maps. Proceedings of the American Mathematical Society, 128 (10). pp. 2947-2956. ISSN 0002-9939.

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We characterize Bers space by means of maximal ϕ-disks. As an application we show that the Hopf differential of a quasiregular harmonic map with respect to strongly negatively curved metric belongs to Bers space. Also we give further sufficient or necessary conditions for a holomorphic function to belong to Bers space.

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Additional Information:© 2000 American Mathematical Society. Received by the editors April 20, 1998 and, in revised form, August 27, 1998 and November 18, 1998. We wish to thank the referee for numerous useful comments and suggestions which greatly improved the exposition of our paper and for pointing out that our results can possibly be of use in a number of popular open problems. We also would like to thank M. Wolf for useful conversations and his interest in this work, A. Baernstein for pointing out to us the Stegenga-Stephenson paper [15] and for helping us to prepare this paper, C.V. Stanojević for his continous encouragement and support during the last few years and B. Hanson for his interest in this work and suggestions concerning the language.
Subject Keywords:Quadratic differentials, Bers space, quasiregular harmonic maps, negatively curved metrics
Issue or Number:10
Classification Code:1991 Mathematics Subject Classification. Primary 30F30; Secondary 32G15, 58E20.
Record Number:CaltechAUTHORS:20170505-114730317
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Official Citation:Uniformly Bounded Maximal φ-Disks, Bers Space and Harmonic Maps I. Anić, V. Marković and M. Mateljević Proceedings of the American Mathematical Society Vol. 128, No. 10 (Oct., 2000), pp. 2947-2956 Published by: American Mathematical Society Stable URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77226
Deposited By: Ruth Sustaita
Deposited On:05 May 2017 19:17
Last Modified:03 Oct 2019 17:55

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