The Journal of Geometric Analysis

, Volume 25, Issue 3, pp 1890–1914 | Cite as

Schwarz Lemma at the Boundary of the Unit Ball in \(\mathbb {C}^n\) and Its Applications

  • Taishun LiuEmail author
  • Jianfei Wang
  • Xiaomin Tang


In this paper, we first establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit ball in \(\mathbb {C}^n\). We then apply our new Schwarz lemma to study problems from the geometric function theory in several complex variables.


Holomorphic mappings Schwarz lemma Convex mappings Unit ball in \(\mathbb {C}^n\)

Mathematics Subject Classification

Primary 32H02 30C80 Secondary 32A30 30C45 



This work is supported by the NNSF of China (Nos. 11031008, 11101139, 11271124, 11001246), NSF of Zhejiang province (Nos.Y14A010047, Y6110260).


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Copyright information

© Mathematica Josephina, Inc. 2014

Authors and Affiliations

  1. 1.Department of MathematicsHuzhou Teachers CollegeHuzhouPeople’s Republic of China
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China

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