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 ℂn 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.
Arosio, L., Bracci, F., Wold, E. (2015). Embedding univalent functions in filtering Loewner chains in higher dimension. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 143(4), 1627-1634 [10.1090/S0002-9939-2014-12339-2].
Embedding univalent functions in filtering Loewner chains in higher dimension
AROSIO, LEANDRO;BRACCI, FILIPPO;
2015-01-01
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 ℂn 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.File in questo prodotto:
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