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    STUDIA MATHEMATICA - Issue no. 2 / 2022  
         
  Article:   SHEARING MAPS AND A RUNGE MAP OF THE UNIT BALL WHICH DOES NOT EMBED INTO A LOEWNER CHAIN WITH RANGE Cn.

Authors:  FILIPPO BRACCI, PAVEL GUMENYUK.
 
       
         
  Abstract:  
DOI: 10.24193/subbmath. 2022.2.03

Published Online: 2022-06-10
Published Print: 2022-06-30
pp. 251-258

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Abstract: In this paper we study the class of ``shearing'''' holomorphic maps of the unit ball of the form $(z,w)mapsto (z+g(w), w)$. Besides general properties, we use such maps to construct an example of a normalized univalent map of the ball onto a Runge domain in $C^n$ which however cannot be embedded into a Loewner chain whose range is $C^n$.

Key words: Loewner chains, geometric function theory, embedding problem

Mathematics Subject Classification (2010): 32H02, 32T15, 32A30, 30C55
 
         
     
         
         
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