Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range $\mathbb C^n$

DOI10.24193/SUBBMATH.2022.2.03arXiv2202.00483MaRDI QIDQ6389850

Pavel Gumenyuk, Filippo Bracci

Publication date: 1 February 2022

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 $mathbb{C}^n$ which however cannot be embedded into a Loewner chain whose range is $mathbb{C}^n$.

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Other generalizations of function theory of one complex variable (32A30) General theory of univalent and multivalent functions of one complex variable (30C55) Strongly pseudoconvex domains (32T15)

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