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Author (up) Efraimidis, I.; Ferrada-Salas, A.; Hernandez, R.; Vargas, R. doi  openurl
  Title Schwarzian derivatives for pluriharmonic mappings Type
  Year 2021 Publication Journal of Mathematical Analysis and Applications Abbreviated Journal J. Math. Anal. Appl.  
  Volume 495 Issue 1 Pages 124716  
  Keywords Pluriharmonic mapping; Pre-Schwarzian derivative; Schwarzian derivative  
  Abstract A pre-Schwarzian and a Schwarzian derivative for locally univalent pluriharmonic mappings in Cn are introduced. Basic properties such as the chain rule, multiplicative invariance and affine invariance are proved for these operators. It is shown that the pre-Schwarzian is stable only with respect to rotations of the identity. A characterization is given for the case when the pre-Schwarzian derivative is holomorphic. Furthermore, it is shown that if the Schwarzian derivative of a pluriharmonic mapping vanishes then the analytic part of this mapping is a Mobius transformation. Some observations are made related to the dilatation of pluriharmonic mappings and to the dilatation of their affine transformations, revealing differences between the theories in the plane and in higher dimensions. An example is given that rules out the possibility for a shear construction theorem to hold in Cn, for n >= 2. (C) 2020 Elsevier Inc. All rights reserved.  
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  ISSN 0022-247X ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1317  
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