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Article
The balanced metrics and cscK metrics on polyball bundles
In this paper, we use the the well-known Calabi ansatz, further generalized by Hwang–Singer and Apostolov–Calderbank–Gauduchon, to study the existence of constant scalar curvature Kähler (cscK for short) metri...
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Article
Special Toeplitz Operators on n-Dimensional Generalized Hartogs Triangles
For given \({\textbf {p}}:=(p_1, \ldots , p_n) \in (\mathbb {Z}^{+})^n\) p ...
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Article
Special Toeplitz operators on a class of bounded Hartogs domains
We introduce a wide class of bounded Hartogs domains in \({\mathbb {C}}^n\)Cn, which contains some generalizations of the classical Hartogs triangle. A sharp criterion for the \(L^p-L^q\)Lp-Lq boundedness of the ...
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Article
The Kobayashi Pseudometric for the Fock–Bargmann–Hartogs Domain and Its Application
The Fock–Bargmann–Hartogs domain \(D_{n,m}\)Dn,m in \(\mathbb {C}^{n+m}\)Cn+m is defined by the inequality \(\Vert w\Vert ^2<e^{-\Vert z\Vert ^2},\)‖w‖2<e-‖z‖2, where $$(z,w)\in \mathbb {C}^n\times \mathbb {C}^m$...
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Article
Weighted Space and Bloch-Type Space on the Unit Ball of an Infinite Dimensional Complex Banach Space
Let \({\mathbf {B}}_{{\mathbb {X}}}\) B ...
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Article
Growth and Distortion Results for a Class of Biholomorphic Map** and Extremal Problem with Parametric Representation in \(\mathbb {C}^n\)
Let \(\widehat{\mathcal {S}}_g^{\alpha , \beta }(\mathbb {B}^n)\) ...
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Article
Classification of Proper Holomorphic Map**s Between Certain Unbounded Non-hyperbolic Domains
The Fock–Bargmann–Hartogs domain \(D_{n,m}(\mu )\) ...
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Article
Balanced metrics on the Fock–Bargmann–Hartogs domains
The Fock–Bargmann–Hartogs domain \(D_{n,m}(\mu )\) ...
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Article
Rigidity of proper holomorphic map**s between equidimensional Hua domains
Hua domain, named after Chinese mathematician Loo-Keng Hua, is defined as a domain in \({\mathbb {C}}^{n}\) ...
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Article
The Weighted Super-Bergman Kernels of \(\mathbb {B}^{m|n}\) and Integral Representations of the Invariant Inner Products on \(H^2_{\nu }(\mathbb {B}^m)\)
The purpose of this paper is twofold. Firstly, we give explicit expressions of the super-Szeg \(\ddot{o}\) ...
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Article
Balanced metrics on some Hartogs type domains over bounded symmetric domains
The definition of balanced metrics was originally given by Donaldson in the case of a compact polarized Kähler manifold in 2001, who also established the existence of such metrics on any compact projective Käh...
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Article
On canonical metrics on Cartan–Hartogs domains
The Cartan–Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan–Hartogs domain
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Article
Uniqueness theorems for meromorphic map**s in several complex variables into P N (ℂ) with two families of moving targets
The authors prove some uniqueness theorems for meromorphic map**s in several complex variables into the complex projective space P N (ℂ) with two families of m...
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Article
Montel-type theorems in several complex variables with continuously moving targets
The authors introduce a new idea related to Montel-type theorems in higher dimension and prove some Montel-type criteria for normal families of holomorphic map**s and normal holomorphic map**s of several c...
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Article
Open AccessFactorization of proper holomorphic maps on irreducible bounded symmetric domains of rank ⩾ 2
We obtain rigidity results on arbitrary proper holomorphic maps F from an irreducible bounded symmetric domain Ω of rank ⩾ 2 into any complex space Z. After lifting to the normalization of the subvariety F(Ω) ⊂ Z
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Article
Characterization of isolated homogeneous hypersurface singularities in ℂ4
Let V be a hypersurface with an isolated singularity at the origin in ℂ n+1. It is a natural question to ask when V is defined by weighted homogeneous polynomial or homogeneous polynomi...
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Article
Normal families of meromorphic map**s of several complex variables into PN (C) for moving targets
Motivated by Ru and Stoll’s accomplishment of the second main theorem in higher dimension with moving targets, many authors studied the moving target problems in value distribution theory and related topics. B...
