Some Properties of Bounded Holomorphic Mappings Defined on Bounded Homogeneous Domains

1986 ◽  
Vol 29 (3) ◽  
pp. 358-364
Author(s):  
Yoshihisa Kubota
Keyword(s):  
Holomorphic Mapping ◽  
Holomorphic Mappings ◽  
Homogeneous Domain ◽  
Homogeneous Domains ◽  
Bounded Holomorphic ◽  
Bounded Homogeneous Domain

AbstractLet F be a bounded holomorphic mapping defined on a bounded homogeneous domain in ℂN. We study the relation between the Jacobian JF(z) and the radius dF(z) of uni valence of F.

Holomorphic Mappings of the Hyperbolic Space into the Complex Euclidean Space and the Bloch Theorem

1975 ◽  
Vol 27 (2) ◽  
pp. 446-458 ◽  
Author(s):  
Kyong T. Hahn
Keyword(s):  
Euclidean Space ◽  
Unit Ball ◽  
Hyperbolic Space ◽  
Holomorphic Mapping ◽  
Continuous Functions ◽  
Holomorphic Mappings ◽  
Euclidean Metric ◽  
The Family ◽  
Complex Euclidean Space ◽  
Bounded Holomorphic

This paper is to study various properties of holomorphic mappings defined on the unit ball B in the complex euclidean space Cn with ranges in the space Cm. Furnishing B with the standard invariant Kähler metric and Cm with the ordinary euclidean metric, we define, for each holomorphic mapping f : B → Cm, a pair of non-negative continuous functions qf and Qf on B ; see § 2 for the definition.Let (Ω), Ω > 0, be the family of holomorphic mappings f : B → Cn such that Qf(z) ≦ Ω for all z ∈ B. (Ω) contains the family (M) of bounded holomorphic mappings as a proper subfamily for a suitable M > 0.

scholarly journals A Note on the Bergman metric of Bounded homogeneous Domains

2007 ◽  
Vol 186 ◽  
pp. 157-163 ◽  
Author(s):  
Chifune Kai ◽  
Takeo Ohsawa
Keyword(s):  
Potential Function ◽  
Bergman Metric ◽  
Homogeneous Domain ◽  
Homogeneous Domains ◽  
Bounded Homogeneous Domain

AbstractWe show that the Bergman metric of a bounded homogeneous domain has a potential function whose gradient has a constant norm with respect to the Bergman metric, and further that this constant is independent of the choice of such a potential function.

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.

Generalization of Schwarz-Pick Lemma to Invariant Volume

1969 ◽  
Vol 21 ◽  
pp. 669-674
Author(s):  
K. T. Hahn ◽  
Josephine Mitchell
Keyword(s):  
Euclidean Space ◽  
Explicit Form ◽  
Bounded Domain ◽  
Kähler Manifold ◽  
Siegel Domain ◽  
Homogeneous Domain ◽  
Kahler Manifold ◽  
Invariant Volume ◽  
Complex Euclidean Space ◽  
Bounded Homogeneous Domain

In this paper we give an extension of (6, Theorem 1), using a similar method of proof, to every homogeneous Siegel domain of second kind which can be mapped biholomorphically into a Kâhler manifold of a certain class (Theorem 1). Then by a well-known result of Vinberg, Gindikin, and Pjateckiï-Sapiro (10) that every bounded homogeneous domain D,contained in a complex euclidean space CN,can be mapped biholomorphically onto an affinely homogeneous Siegel domain of second kind, the theorem follows for D(Theorem 2). (6, Theorem 1) is a generalization of the Ahlfors version of the Schwarz-Pick lemma in C1(1) to invariant volume for a star-like homogeneous bounded domain in CN;see also (4). In § 3 we give the inequality for a special non-symmetric Siegel domain of second kind using an explicit form of TD(z, )due to Lu (7).

scholarly journals Algebraic degeneracy theorem for holomorphic mappings into smooth projective algebraic varieties

1981 ◽  
Vol 84 ◽  
pp. 209-218
Author(s):  
Yoshihiro Aihara ◽  
Seiki Mori
Keyword(s):  
General Position ◽  
Holomorphic Mapping ◽  
Holomorphic Mappings ◽  
Holomorphic Curve ◽  
Algebraic Varieties ◽  
Picard Theorem ◽  
Picard’S Theorem ◽  
Picard's Theorem ◽  
Algebraic Degeneracy

The famous Picard theorem states that a holomorphic mapping f: C → P1(C) omitting distinct three points must be constant. Borel [1] showed that a non-degenerate holomorphic curve can miss at most n + 1 hyperplanes in Pn(C) in general position, thus extending Picard’s theorem (n = 1). Recently, Fujimoto [3], Green [4] and [5] obtained many Picard type theorems using Borel’s methods for holomorphic mappings.

Bergman–Hartogs domains and their automorphisms

2019 ◽  
pp. 316-323
Author(s):  
Guy ROOS
Keyword(s):  
Automorphism Groups ◽  
Symmetric Domain ◽  
Bounded Symmetric Domain ◽  
Homogeneous Domain ◽  
Hartogs Domains ◽  
Bounded Homogeneous Domain

For Cartan–Hartogs domains and also for Bergman–Hartogs domains, the determination of their automorphism groups is given for the cases when the base is any bounded symmetric domain and a general bounded homogeneous domain respectively.

THE NUMBERS OF PERIODIC ORBITS HIDDEN AT FIXED POINTS OF THREE-DIMENSIONAL HOLOMORPHIC MAPPINGS

2010 ◽  
Vol 21 (05) ◽  
pp. 571-590
Author(s):  
GUANG YUAN ZHANG
Keyword(s):  
Fixed Point ◽  
Positive Integer ◽  
Periodic Orbits ◽  
Holomorphic Mapping ◽  
Three Dimensional ◽  
Holomorphic Mappings ◽  
Necessary Condition ◽  
Roots Of Unity ◽  
Number Formula ◽  
Sufficient And Necessary Condition

Let M be a positive integer and let f be a holomorphic mapping from a ball Δn = {x ∈ ℂn;|x| < δ} into ℂn such that the origin 0 is an isolated fixed point of both f and the M-th iteration fM of f. Then one can define the number [Formula: see text], which can be interpreted to be the number of periodic orbits of f with period M hidden at the fixed point 0. For a 3 × 3 matrix A, of which the eigenvalues are all distinct primitive M-th roots of unity, we will give a sufficient and necessary condition for A such that for any holomorphic mapping f: Δ 3 → ℂ3 with f(0) = 0 and Df(0) = A, if 0 is an isolated fixed point of the M-th iteration fM, then [Formula: see text].

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