In this paper we study the class of "shearing" holomorphic maps of the unit ball of the form (z ,w) bar right arrow (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.
Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range C-n / Filippo Bracci; Pavel Gumenyuk. - In: STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA. - ISSN 0252-1938. - 67:(2022), pp. 251-258. [10.24193/subbmath.2022.2.03]
Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range C-n
Filippo Bracci;
2022
Abstract
In this paper we study the class of "shearing" holomorphic maps of the unit ball of the form (z ,w) bar right arrow (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.
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