Language：English   Publishing type：Research paper (scientific journal)   Publisher：SPRINGER  

We study invariant metrics on unbounded strongly pseudoconvex domains with non-compact automorphism group. The main result is that the corresponding Bergman and Khler-Einstein metrics are metrically equivalent. We also determine the comparisons among invariant metrics, including the Carath,odory and Kobayashi pseudo-metrics additionally.

DOI： 10.1007/s10455-016-9511-7

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：MATHEMATICAL ASSOC AMER  

This note gives a concise proof of a classical Poincare's theorem which asserts that the unit ball B-2 and the polydisk D x D are not holomorphically equivalent.

DOI： 10.4169/amer.math.monthly.122.10.1003

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

Applying a theorem due to Diederich and Ohsawa on weighted Bergman kernels, we characterize some Hartogs domains by their holomorphic automorphisms. (C) 2014 Elsevier Masson SAS. All rights reserved.

DOI： 10.1016/j.bulsci.2014.11.007

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

A theorem due to Cartan asserts that every origin-preserving automorphism of bounded circular domains with respect to the origin is linear. In the present paper, by employing the theory of Bergman's representative domain, we prove that under certain circumstances Cartan's assertion remains true for quasi-circular domains in C-n. Our main result is applied to obtain some simple criterions for the case n = 3 and to prove that Braun-Kaup-Upmeier's theorem remains true for our class of quasi-circular domains. (C) 2015 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.jmaa.2015.01.061

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER MATHEMATICAL SOC  

We establish a series representation formula of the Bergman kernel of a certain class of domains, which generalizes the Forelli-Rudin construction of the Hartogs domain. Our formula is applied to derive deflation type identities of the Bergman kernels for our domains.

DOI： 10.1090/S0002-9939-2014-12317-3

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：SPRINGER  

This is a short survey article on Cartan's theorem about automorphisms fixing the origin for certain class of quasi-circular domains and non-hyperbolic circular domains. Some open problems are also given.

DOI： 10.1007/978-4-431-55744-9_26

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

It was shown by Kaup that every origin-preserving automorphism of quasi-circular domains is a polynomial mapping. In this paper, we study how the weight of quasi-circular domains and the degree of such automorphisms are related. By using the Bergman mapping, we prove that every origin-preserving automorphism of normal quasi-circular domains in C-2 is linear. (C) 2013 Elsevier Masson SAS. All rights reserved.

DOI： 10.1016/j.bulsci.2013.10.002

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ACADEMIC PRESS INC ELSEVIER SCIENCE  

In this paper we determine the automorphism group of the Fock-Bargmann-Hartogs domain D-n,D-m in C-n x C-m which is defined by the inequality parallel to delta parallel to(2) < e(-mu parallel to z parallel to 2). (c) 2013 Elsevier Inc. All rights reserved.

DOI： 10.1016/j.jmaa.2013.07.007

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：TAYLOR & FRANCIS LTD  

We consider the FockBargmannHartogs domain D-n,D-m which is defined by the inequality where (z,)C(n)xC(m) and >0. We give an explicit formula for the Bergman kernel of the domain in terms of the polylogarithm functions. Moreover, using the interlacing property, we describe how the existence of zeros of the Bergman kernel depends on the integers m and n.

DOI： 10.1080/17476933.2011.620098

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER  

We give an explicit formula of the Bergman kernel of a certain Hartogs domain. (C) 2012 Published by Elsevier Masson SAS on behalf of Academie des sciences.

DOI： 10.1016/j.crma.2012.10.009

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER  

We give a new formula for the Bergman kernels of the Cartan-Hartogs domains. As an application of our formula, we study the Lu Qi-Keng problem of the Cartan-Hartogs domains. (C) 2012 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

DOI： 10.1016/j.crma.2012.01.005

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Language：English   Publishing type：Research paper (scientific journal)  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：HIROSHIMA UNIV, GRAD SCH SCI  

We develop a group-theoretic method to generalize the Laplace-Beltrami operators on the classical domains. In [11], inspired by Helgason's paper [3], we defined the "Poisson transforms'' for homogeneous vector bundles over symmetric spaces. In [13], we defined the generalized Poisson-Cauchy transforms for homogeneous holomorphic line bundles over hermitian symmetric spaces and computed explicitly the kernel functions for each type of the classical domains. In [7], making use of the Casimir operator, we defined the "generalized Laplacians'' on homogeneous holomorphic line bundles over hermitian symmetric spaces and showed that the generalized Poisson-Cauchy transforms give rise to eigenfunctions of the "generalized Laplacians''. In this paper, using the canonical coordinates for each type of the classical domains, we carry out the direct computation to obtain the explicit formulas of ( line bundle valued) invariant differential operators which we call the generalized Laplacians and compute their eigenvalues evaluated at the generalized Poisson-Cauchy kernel functions.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：JAPAN ACAD  

We develop a group-theoretic method of generalizing the Laplace-Beltrami operators on the classical domains. In [18], we defined the generalized Poisson-Cauchy transforms on the classical domains. We show that the generalized Poisson-Cauchy transforms give us eigenfunctions of the generalized Laplacians defined in this paper.

DOI： 10.3792/pjaa.82.167

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