scholarly journals Proper holomorphic maps from the unit disk to some unit ball

2016 ◽  
Vol 145 (6) ◽  
pp. 2649-2660 ◽  
Author(s):  
John P. D’Angelo ◽  
Zhenghui Huo ◽  
Ming Xiao
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Holomorphic Maps ◽  
Proper Holomorphic Maps

scholarly journals On the Singular Loci and the Images of Proper Holomorphic Maps From Pseudoellipsoids

2015 ◽  
Vol 117 (2) ◽  
pp. 170
Author(s):  
Cristina Giannotti ◽  
Andrea Spiro
Keyword(s):  
Unit Ball ◽  
Holomorphic Maps ◽  
Proper Holomorphic Maps ◽  
Singular Loci

We prove a generalisation of Rudin's theorem on proper holomorphic maps from the unit ball to the case of proper holomorphic maps from pseudoellipsoids.

scholarly journals On Critical Points of Proper Holomorphic Maps on The Unit Disk

1998 ◽  
Vol 30 (1) ◽  
pp. 62-66 ◽  
Author(s):  
Saeed Zakeri
Keyword(s):  
Unit Disk ◽  
Critical Points ◽  
Holomorphic Maps ◽  
Proper Holomorphic Maps

scholarly journals Proper holomorphic maps between bounded symmetric domains revisited

2014 ◽  
Vol 271 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Gautam Bharali ◽  
Jaikrishnan Janardhanan
Keyword(s):  
Holomorphic Maps ◽  
Bounded Symmetric Domains ◽  
Proper Holomorphic Maps

scholarly journals The linearity of proper holomorphic maps between balls in the low codimension case

1986 ◽  
Vol 24 (1) ◽  
pp. 15-17 ◽  
Author(s):  
James J. Faran
Keyword(s):  
Holomorphic Maps ◽  
Proper Holomorphic Maps

scholarly journals Landau’s theorem for slice regular functions on the quaternionic unit ball

2017 ◽  
Vol 28 (03) ◽  
pp. 1750017 ◽  
Author(s):  
Cinzia Bisi ◽  
Caterina Stoppato
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Analogous Result ◽  
Open Unit ◽  
Open Unit Ball ◽  
Slice Regular Functions ◽  
New Approach ◽  
The Real ◽  
Regular Functions ◽  
Real Algebra

During the development of the theory of slice regular functions over the real algebra of quaternions [Formula: see text] in the last decade, some natural questions arose about slice regular functions on the open unit ball [Formula: see text] in [Formula: see text]. This work establishes several new results in this context. Along with some useful estimates for slice regular self-maps of [Formula: see text] fixing the origin, it establishes two variants of the quaternionic Schwarz–Pick lemma, specialized to maps [Formula: see text] that are not injective. These results allow a full generalization to quaternions of two theorems proven by Landau for holomorphic self-maps [Formula: see text] of the complex unit disk with [Formula: see text]. Landau had computed, in terms of [Formula: see text], a radius [Formula: see text] such that [Formula: see text] is injective at least in the disk [Formula: see text] and such that the inclusion [Formula: see text] holds. The analogous result proven here for slice regular functions [Formula: see text] allows a new approach to the study of Bloch–Landau-type properties of slice regular functions [Formula: see text].

Linearity and Second Fundamental Forms for Proper Holomorphic Maps from $\mathbb{B}^{n+1}$ to $\mathbb{B}^{4n-3}$

2011 ◽  
Vol 22 (4) ◽  
pp. 977-1006 ◽  
Author(s):  
Xiaoliang Cheng ◽  
Shanyu Ji
Keyword(s):  
Holomorphic Maps ◽  
Proper Holomorphic Maps

scholarly journals On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qing-Hua Xu ◽  
Tai-Shun Liu
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Unit Disk ◽  
Univalent Functions ◽  
Complex Banach Space ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Unit Polydisk ◽  
Starlike Mappings

LetSbe the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known resultmaxf∈S⁡a3-λa22=1+2e-2λ/(1-λ)forλ∈0, 1. We investigate the corresponding problem for the class of starlike mappings defined on the unit ball in a complex Banach space or on the unit polydisk inCn, which satisfies a certain condition.

Proper holomorphic maps from weakly pseudoconvex domains

1990 ◽  
Vol 60 (2) ◽  
pp. 363-388 ◽  
Author(s):  
Alan Noell ◽  
Berit Stens�nes
Keyword(s):  
Pseudoconvex Domains ◽  
Holomorphic Maps ◽  
Proper Holomorphic Maps ◽  
Weakly Pseudoconvex

Classification of proper holomorphic maps between Reinhardt domains in ${\Bbb C}^2$

1998 ◽  
Vol 227 (1) ◽  
pp. 27-44 ◽  
Author(s):  
Andrea Spiro
Keyword(s):  
Holomorphic Maps ◽  
Reinhardt Domains ◽  
Proper Holomorphic Maps
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