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.

Bracci, F., Gumenyuk, P. (2022). Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range C-n. STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA, 67(2), 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
;
2022-01-01

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.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Loewner chains
geometric function theory
embedding problem
Bracci, F., Gumenyuk, P. (2022). Shearing maps and a Runge map of the unit ball which does not embed into a Loewner chain with range C-n. STUDIA UNIVERSITATIS BABES-BOLYAI. MATHEMATICA, 67(2), 251-258 [10.24193/subbmath.2022.2.03].
Bracci, F; Gumenyuk, P
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/327503
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