Embedding univalent functions in filtering Loewner chains in higher dimension

Arosio, Leandro; Bracci, Filippo; Wold, Erlend

doi:10.1090/S0002-9939-2014-12339-2

Embedding univalent functions in filtering Loewner chains in higher dimension
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by Leandro Arosio, Filippo Bracci and Erlend Fornæss Wold PDF

Proc. Amer. Math. Soc. 143 (2015), 1627-1634 Request permission

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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