We prove (and improve) the Muir-Suffridge conjecture for holomorphic convex maps. Namely, let F : B-n -> C-n be a univalent map from the unit ball whose image D is convex. Let S Bn be the set of points. such that limz.. F(z) = 8. Then we prove that S is either empty, or contains one or two points and F extends as a homeomorphism (F) over tilde : (B) over barn S -> (D) over bar. Moreover, S = empty set if D is bounded, S has one point if D has one connected component at infinity and S has two points if D has two connected components at infinity and, up to composition with an automorphism of the ball and renormalization, F is an extension of the strip map in the plane to higher dimension.

Bracci, F., Gaussier, H. (2018). A proof of the Muir–Suffridge conjecture for convex maps of the unit ball in Cn. MATHEMATISCHE ANNALEN, 372(1-2), 845-858 [10.1007/s00208-017-1581-8].

A proof of the Muir–Suffridge conjecture for convex maps of the unit ball in Cn

Bracci F.
;
2018-01-01

Abstract

We prove (and improve) the Muir-Suffridge conjecture for holomorphic convex maps. Namely, let F : B-n -> C-n be a univalent map from the unit ball whose image D is convex. Let S Bn be the set of points. such that limz.. F(z) = 8. Then we prove that S is either empty, or contains one or two points and F extends as a homeomorphism (F) over tilde : (B) over barn S -> (D) over bar. Moreover, S = empty set if D is bounded, S has one point if D has one connected component at infinity and S has two points if D has two connected components at infinity and, up to composition with an automorphism of the ball and renormalization, F is an extension of the strip map in the plane to higher dimension.
2018
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
https://link.springer.com/article/10.1007/s00208-017-1581-8
Bracci, F., Gaussier, H. (2018). A proof of the Muir–Suffridge conjecture for convex maps of the unit ball in Cn. MATHEMATISCHE ANNALEN, 372(1-2), 845-858 [10.1007/s00208-017-1581-8].
Bracci, F; Gaussier, H
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/216087
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