Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range Cⁿ
DOI:
https://doi.org/10.24193/subbmath.2022.2.03Keywords:
Loewner chains, geometric function theory, embedding problem.Abstract
In this paper we study the class of “shearing” holomorphic maps of the unit ball of the form (z, w) i→ (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 Cn which however cannot be embedded into a Loewner chain whose range is Cn.
Mathematics Subject Classification (2010): 32H02, 32T15, 32A30, 30C55.
Received 2 February 2022; Accepted 9 March 2022.
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