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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniformly bounded maximal $\varphi$-disks, Bers space and harmonic maps


Authors: I. Anic, V. Markovic and M. Mateljevic
Journal: Proc. Amer. Math. Soc. 128 (2000), 2947-2956
MSC (1991): Primary 30F30; Secondary 32G15, 58E20
Published electronically: April 7, 2000
MathSciNet review: 1664317
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Abstract:

We characterize Bers space by means of maximal $\varphi $-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

I. Anic
Affiliation: Faculty of Mathematics, University of Belgrade, Studentski Trg 16, Belgrade, Yugoslavia
Email: ianic@matf.bg.ac.yu

V. Markovic
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: markovic@math.umn.edu

M. Mateljevic
Affiliation: Faculty of Mathematics, University of Belgrade, Studentski Trg 16, Belgrade, Yugoslavia
Email: miodrag@matf.bg.ac.yu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05325-9
PII: S 0002-9939(00)05325-9
Keywords: Quadratic differentials, Bers space, quasiregular harmonic maps, negatively curved metrics
Received by editor(s): April 20, 1998
Received by editor(s) in revised form: August 27, 1998, and November 18, 1998
Published electronically: April 7, 2000
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society