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A Schwarz Lemma for Harmonic Mappings Between the Unit Balls in Real Euclidean Spaces

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Abstract

The authors prove a Schwarz lemma for harmonic mappings between the unit balls in real Euclidean spaces. Roughly speaking, this result says that under a harmonic mapping between the unit balls in real Euclidean spaces, the image of a smaller ball centered at origin can be controlled. This extends the related result proved by Chen in complex plane.

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Acknowledgement

The authors would like to thank the professor Chen Zhihua for his valuable suggestions.

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 210096, China

    Shaoyu Dai

  2. Department of Mathematics, Jinling Institute of Technology, Nanjing, 211169, China

    Shaoyu Dai

  3. Department of Mathematical Sciences, Purdue University Fort Wayne, Purdue, IN, 46805-1499, USA

    Yifei Pan

Authors
  1. Shaoyu Dai
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  2. Yifei Pan
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Corresponding author

Correspondence to Shaoyu Dai.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11201199, 11671361).

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Dai, S., Pan, Y. A Schwarz Lemma for Harmonic Mappings Between the Unit Balls in Real Euclidean Spaces. Chin. Ann. Math. Ser. B 39, 1065–1092 (2018). https://doi.org/10.1007/s11401-018-0114-4

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  • DOI: https://doi.org/10.1007/s11401-018-0114-4

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