• 대한수학회지
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• 제44권6호
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• pp.1291-1312
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• 2007

We study some extremal problems on the Cartan-Hartogs domains. Through computing the minimal circumscribed Hermitian ellipsoid of the Cartan-Hartogs domains, we get the $Carath\acute{e}odory$ extremal mappings between the Cartan-Hartogs domains and the unit hyperball, and the explicit formulas for computing the $Carath\acute{e}odory$ extremal value.

• 대한수학회지
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• 제58권6호
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• pp.1347-1365
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• 2021

For µ = (µ₁, …, µ_t) (µ_j > 0), ξ = (z₁, …, z_t, w) ∈ ℂ^n₁ × … × ℂ^n_t × ℂ^m, define $${\Omega}({\mu},t)=\{{\xi}{\in}\mathbb{B}_{n_1}{\times}{\cdots}{\times}\mathbb{B}_{n_t}{\times}\mathbb{C}^m:{\parallel}w{\parallel}^2 where $\mathbb{B}_{n_j}$ is the unit ball in ℂ^n_j (1 ≤ j ≤ t), C(χ, µ) is a constant only depending on χ = (n₁, …, n_t) and µ = (µ₁, …, µ_t), which is a special type of generalized Cartan-Hartogs domain. We will give some sufficient and necessary conditions for the boundedness of some type of operators on L^p(Ω(µ, t), ω) (the weighted L^p space of Ω(µ, t) with weight ω, 1 < p < ∞). This result generalizes the works from certain classes of generalized complex ellipsoids to the generalized Cartan-Hartogs domain Ω(µ, t).

• East Asian mathematical journal
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• 제28권3호
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• pp.347-352
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• 2012

In this paper, we introduce techniques for computations of the automorphism group of special doamins, for example the Kohn-Nirenberg domain, Fornaess domain and Cartan Hartogs domain.

• 대한수학회지
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• 제40권4호
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• pp.609-627
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• 2003

In this paper we describe the Einstein-Kahler metric for the Cartan-Hartogs of the first type which is the special case of the Hua domains. Firstly, we reduce the Monge-Ampere equation for the metric to an ordinary differential equation in the auxiliary function X = X(z, w) = $\midw\mid^2[det(I-ZZ^{T}]^{\frac{1}{K}}$ (see below). This differential equation can be solved to give an implicit function in Χ. Secondly, we get the estimate of the holomorphic section curvature under the complete Einstein-K$\ddot{a}$hler metric on this domain.