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

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.
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: http://hdl.handle.net/2108/242259
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