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Embedding univalent functions in filtering Loewner chains in higher dimension


Authors: Leandro Arosio, Filippo Bracci and Erlend Fornæss Wold
Journal: Proc. Amer. Math. Soc. 143 (2015), 1627-1634
MSC (2010): Primary 32H02, 32T15, 32A30, 30C55
DOI: https://doi.org/10.1090/S0002-9939-2014-12339-2
Published electronically: November 12, 2014
MathSciNet review: 3314075
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Abstract: We discuss the problem of embedding univalent functions into Loewner chains in higher dimension. In particular, we prove that a normalized univalent map of the ball in $ \mathbb{C}^n$ whose image is a smooth strongly pseudoconvex domain is embeddable into a normalized Loewner chain (also satisfying some extra regularity properties) if and only if the closure of the image is polynomially convex.


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Additional Information

Leandro Arosio
Affiliation: Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy
Email: arosio@mat.uniroma2.it

Filippo Bracci
Affiliation: Dipartimento Di Matematica, Università di Roma “Tor Vergata”, Via Della Ricerca Scientifica 1, 00133, Roma, Italy
Email: fbracci@mat.uniroma2.it

Erlend Fornæss Wold
Affiliation: Matematisk Institutt, Universitetet i Oslo, Postboks 1053 Blindern, 0316 Oslo, Norway
Email: erlendfw@math.uio.no

DOI: https://doi.org/10.1090/S0002-9939-2014-12339-2
Keywords: Loewner theory, embedding problems, univalent functions, polynomially convex domains, Runge domains
Received by editor(s): June 26, 2013
Received by editor(s) in revised form: August 21, 2013
Published electronically: November 12, 2014
Additional Notes: The first and second authors were supported by ERC grant “HEVO - Holomorphic Evolution Equations” n. 277691
The third author was supported by NFR grant 209751/F20
Communicated by: Franc Forstneric
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.