Proper Holomorphic Mappings of Complex Spaces

1998 ◽  
pp. 1-38 ◽  
Author(s):  
Steven R. Bell ◽  
Raghavan Narasimhan
Keyword(s):  
Holomorphic Mappings ◽  
Complex Spaces ◽  
Proper Holomorphic Mappings

scholarly journals Proper holomorphic mappings between complex spaces

2015 ◽  
Vol 45 (11) ◽  
pp. 1877-1880
Author(s):  
ZhenQian LI ◽  
HuiPing ZHANG
Keyword(s):  
Holomorphic Mappings ◽  
Complex Spaces ◽  
Proper Holomorphic Mappings

Proper holomorphic mappings and related automorphism groups

1997 ◽  
Vol 7 (4) ◽  
pp. 623-636 ◽  
Author(s):  
K. Oeljeklaus ◽  
E. H. Youssfi
Keyword(s):  
Automorphism Groups ◽  
Holomorphic Mappings ◽  
Proper Holomorphic Mappings

scholarly journals SCHWARZ LEMMA FOR HOLOMORPHIC MAPPINGS IN THE UNIT BALL

2017 ◽  
Vol 60 (1) ◽  
pp. 219-224 ◽  
Author(s):  
DAVID KALAJ
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Type Inequality ◽  
Holomorphic Mappings ◽  
Schwarz Lemma ◽  
Complex Spaces

AbstractIn this note, we establish a Schwarz–Pick type inequality for holomorphic mappings between unit balls Bn and Bm in corresponding complex spaces. We also prove a Schwarz-Pick type inequality for pluri-harmonic functions.

Fredholm composition operators and proper holomorphic mappings

2019 ◽  
Vol 51 (6) ◽  
pp. 1104-1112 ◽  
Author(s):  
Guangfu Cao ◽  
Li He ◽  
Kehe Zhu
Keyword(s):  
Composition Operators ◽  
Holomorphic Mappings ◽  
Proper Holomorphic Mappings

The Topological Nature of Two Noguchi Theorems on Sequences of Holomorphic Mappings Between Complex Spaces

1995 ◽  
Vol 47 (6) ◽  
pp. 1240-1252
Author(s):  
James E. Joseph ◽  
Myung H. Kwack
Keyword(s):  
Function Theory ◽  
Riemann Sphere ◽  
Complex Function ◽  
Holomorphic Extension ◽  
Holomorphic Mappings ◽  
Classical Theorem ◽  
Complex Function Theory ◽  
Topological Methods ◽  
Complex Spaces ◽  
Picard Theorem

AbstractLet C,D,D* be, respectively, the complex plane, {z ∈ C : |z| < 1}, and D — {0}. If P1(C) is the Riemann sphere, the Big Picard theorem states that if ƒ:D* → P1(C) is holomorphic and P1(C) → ƒ(D*) n a s more than two elements, then ƒ has a holomorphic extension . Under certain assumptions on M, A and X ⊂ Y, combined efforts of Kiernan, Kobayashi and Kwack extended the theorem to all holomorphic ƒ: M → A → X. Relying on these results, measure theoretic theorems of Lelong and Wirtinger, and other properties of complex spaces, Noguchi proved in this context that if ƒ: M → A → X and ƒn: M → A → X are holomorphic for each n and ƒn → ƒ, then . In this paper we show that all of these theorems may be significantly generalized and improved by purely topological methods. We also apply our results to present a topological generalization of a classical theorem of Vitali from one variable complex function theory.

scholarly journals On proper holomorphic mappings from domains with T-action

1999 ◽  
Vol 154 ◽  
pp. 57-72 ◽  
Author(s):  
Bernard Coupet ◽  
Yifei Pan ◽  
Alexandre Sukhov
Keyword(s):  
Unit Circle ◽  
Finite Type ◽  
Holomorphic Mapping ◽  
Circular Domain ◽  
Holomorphic Mappings ◽  
Pseudoconvex Domains ◽  
Branch Locus ◽  
Proper Holomorphic Mapping ◽  
Proper Holomorphic Mappings

AbstractWe describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.

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