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Author (up) Bravo, V.; Hernandez, R.; Venegas, O. pdf  doi
openurl 
  Title On the univalence of certain integral for harmonic mappings Type
  Year 2017 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.  
  Volume 455 Issue 1 Pages 381-388  
  Keywords Harmonic mapping; Univalent functions; Integral transform  
  Abstract We generalize the problem of univalence of the integral of f'(z)(alpha) when f is univalent to the complex harmonic mappings. To do this, we extend the univalence criterion by Ahlfors in [1] to those mappings. (C) 2017 Elsevier Inc. All rights reserved.  
  Address [Bravo, Victor] Univ Valparaiso, Inst Matemat, Fac Ciencias, Valparaiso, Chile, Email: victor.bravo@uv.cl;  
  Corporate Author Thesis  
  Publisher Academic Press Inc Elsevier Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0022-247x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000424735900019 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 826  
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Author (up) Chuaqui, M.; Hernandez, R. pdf  doi
openurl 
  Title The order of a linearly invariant family in C-n Type
  Year 2013 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.  
  Volume 398 Issue 1 Pages 372-379  
  Keywords Linearly invariant family; Bergman metric; Schwarzian operator; Trace order; Variational method; Extremal mapping  
  Abstract We study the (trace) order of the linearly invariant family in the ball B-n defined by parallel to SF parallel to <= alpha, where F : B-n -> C-n is locally biholomorphic and SF is the Schwarzian operator. By adapting Pommerenke's approach, we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of alpha and the dimension n. Lower bounds for the order are established in similar terms by means of examples. (C) 2012 Elsevier Inc. All rights reserved.  
  Address [Chuaqui, Martin] Pontificia Univ Catolica Chile, Fac Matemat, Santiago 22, Chile, Email: mchuaqui@mat.puc.cl;  
  Corporate Author Thesis  
  Publisher Academic Press Inc Elsevier Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0022-247x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000310659500031 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 252  
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Author (up) Chuaqui, M.; Hernandez, R. pdf  doi
openurl 
  Title Univalent harmonic mappings and linearly connected domains Type
  Year 2007 Publication Journal Of Mathematical Analysis And Applications Abbreviated Journal J. Math. Anal. Appl.  
  Volume 332 Issue 2 Pages 1189-1194  
  Keywords harmonic mapping; univalent; linearly connected domain; second complex dilatation  
  Abstract We investigate the relationship between the univalence of f and of h in the decomposition f = h + (g) over bar of a serise-preserving harmonic mapping defined in the unit disk D subset of C. Among other results, we determine the holomorphic univalent maps It for which there exists c > 0 such that every harmonic mapping of the form f = h + (g) over bar with vertical bar g'vertical bar < c vertical bar h'vertical bar is univalent. The notion of a linearly connected domain appears in our study in a relevant way. (c) 2006 Elsevier Inc. All rights reserved.  
  Address Catholic Univ Chile, Santiago, Chile, Email: m.chuaqui@mat.puc.cl  
  Corporate Author Thesis  
  Publisher Academic Press Inc Elsevier Science Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0022-247x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000247120600031 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 42  
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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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0022-247X ISBN Medium  
  Area Expedition Conference  
  Notes Approved  
  Call Number UAI @ alexi.delcanto @ Serial 1317  
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