—Holomorphic mappings of complex spaces

1966 ◽  
pp. 123-136
Author(s):  
Raghavan Narasimhan
Keyword(s):  
Holomorphic Mappings ◽  
Complex Spaces

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.

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 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

HARTOGS-TYPE EXTENSION THEOREMS FOR SEPARATELY HOLOMORPHIC MAPPINGS ON COMPACT SETS

2000 ◽  
Vol 11 (05) ◽  
pp. 723-735 ◽  
Author(s):  
DO DUC THAI ◽  
NGUYEN THI TUYET MAI
Keyword(s):  
Extension Property ◽  
Holomorphic Mappings ◽  
Compact Sets ◽  
Extension Theorems ◽  
Complex Spaces

We give several Hartogs-type extension theorems for separately holomorphic mappings on compact sets into complex spaces which either have the Hartogs extension property or are weakly Brody hyperbolic. Moreover, a characterization for the Hartogs extension property of holomorphically convex Kähler complex spaces by separate analyticity is given.

scholarly journals Normal holomorphic mappings and classical theorems of function theory

1984 ◽  
Vol 94 ◽  
pp. 89-104 ◽  
Author(s):  
Ken-Ichi Funahashi
Keyword(s):  
Nevanlinna Theory ◽  
Meromorphic Functions ◽  
Function Theory ◽  
Hyperbolic Manifolds ◽  
Holomorphic Mappings ◽  
Main Concern ◽  
Boundary Behaviour ◽  
Complex Spaces ◽  
Higher Dimensional ◽  
Classical Function

In [7], O. Lehto and K. I. Virtanen introduced the concept of normal meromorphic functions in connection with the study of boundary behaviour of meromorphic functions of one complex variable.In this paper, we generalize the theory of normal meromorphic functions to the case of holomorphic mappings into higher dimensional complex spaces in connection with the theory of hyperbolic manifolds and Nevanlinna theory.The main concern of this paper is the generalizations of the big Picard theorem and Lindelöf’s theorem which appear in the classical function theory.

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