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The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings

Authors: Huaihui Chen and Paul M. Gauthier
Journal: Proc. Amer. Math. Soc. 139 (2011), 583-595
MSC (2010): Primary 30C99; Secondary 30C62
Published electronically: August 26, 2010
MathSciNet review: 2736340
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Abstract: For a normalized quasiregular pluriharmonic mapping $ f$ of the unit ball $ B^n$ of $ \mathbb{C}^n$ into $ \mathbb{C}^n$, we estimate the supremum of numbers $ R$ such that some subdomain $ \Omega$ of the ball is mapped by $ f$ diffeomorphically onto some ball of radius $ R$. Our estimates significantly improve earlier estimates, even in the case of harmonic functions in the disc.

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Additional Information

Huaihui Chen
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing, Jiangsu, 210097, People’s Republic of China

Paul M. Gauthier
Affiliation: Département de Mathématiques et de Statistique, Université de Montréal, CP 6128-Centreville, Montreal, QC, H3C 3J7 Canada

Keywords: Bloch constant, harmonic mappings
Received by editor(s): March 11, 2010
Published electronically: August 26, 2010
Additional Notes: This research was supported in part by NSFC (China, Grant No. 10671093) and NSERC (Canada)
Communicated by: Mario Bonk
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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