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.
2015
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Embedding problems; Loewner theory; Polynomially convex domains; Runge domains; Univalent functions; Mathematics (all); Applied Mathematics
http://www.ams.org/journals/proc/2015-143-04/S0002-9939-2014-12339-2/S0002-9939-2014-12339-2.pdf
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].
Arosio, L; Bracci, F; Wold, E
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/242259
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