CLASSIFICATION OF A CLASS OF HYPERBOLIC REINHARDT DOMAINS

In this article, the author discusses the dimension of holomorphic automorphism groups on hyperbolic Reirihardt domains. and classifies those hyperbolic Reinhardt domains whose automorphism group has prescribed dimension n2 - 2 (where n is the dimension of domain).     

Serre Problem for Unbounded Pseudoconvex Reinhardt Domains in ℂ<Superscript>2</Superscript>

We give a characterization of non-hyperbolic pseudoconvex Reinhardt domains in ℂ² for which the answer to the Serre problem is positive. Moreover, all non-hyperbolic pseudoconvex Reinhardt domains in ℂ² with non-compact automorphism group are explicitly described.     

On hyperbolicity of pseudoconvex Reinhardt domains

We give a characterization of Kobayashi hyperbolicity of pseudoconvex Reinhardt domains. All such domains turn out to be biholomorphic to a bounded Reinhardt domain. In particular, any Kobayashi hyperbolic pseudoconvex Reinhardt domain is Kobayashi complete.     

A characterization of products of balls by their isotropy groups

In this paper we will characterize products of balls – especially the ball and the polydisc – in by properties of the isotropy group of a single point. It will be shown that such a characterization is possible in the class of Siegel domains of the second kind, a class that extends the class of bounded homogeneous domains, and that such a characterization is no longer possible in the class of bounded domains with noncompact automorphism groups. The main result is that a Siegel domain of the second kind is biholomorphically equivalent to a product of balls, iff there is a point such that the isotropy group of p contains a torus of dimension n. As an application it will be proved that the only domains biholomorphically equivalent to a Siegel domain of the second kind and to a Reinhardt domain are exactly the domains biholomorphically equivalent to a product of b alls. Received: 27 February 1998 / In final form: 6 August 1998     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in ℂ2

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in ?² is an automorphism.     

有界对称域上的VMOp与VO空间的乘子

该文利用 Berezin变换,自同构群及Bergman再生核理论,对有界对称域上的VMO^p与VO空间的点态乘子进行了刻划     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in C~2

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in C~2 is an automorphism.     

阿贝尔群与极大类p-群的半直积的Coleman自同构

设G=A\×P是阿贝尔群$A$与极大类p -群P的半直积,其中P中的元以幂自同构的方式作用于A. 该文证明了G的每个Coleman自同构都是内自同构.作为该结果的一个直接推论, 作者得到了这样的群$G$有正规化子性质.     

Über Fixpunkte holomorpher Automorphismen

Each holomorphic automorphism of an arbitrary domain GS², which has three distinct fixed points in G, reduces to the identity. This is known for domains of finite connectivity and is here proved in full generality by means of the Poincaré-metric of hyperbolic domains and some simple results of Riemannian Geometry.     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in ℂn

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain of D’Angelo finite type in ℂⁿ (n1) is an automorphism.

     

On measures of maximal and full dimension for polynomial automorphisms of

For a hyperbolic polynomial automorphism of , we show the existence of a measure of maximal dimension and identify the conditions under which a measure of full dimension exists.

     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in ?2

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain in ℂ² is an automorphism. The first author’s work was supported in part by the National Natural Science Foundation of China (Grant No. 10571135) and the Doctoral Program Foundation of the Ministry of Education of China (Grant No. 20050240711)     

Complex<Emphasis Type="BoldItalic">n</Emphasis>-dimensional manifolds with a real<Emphasis Type="BoldItalic">n</Emphasis><Superscript>2</Superscript>-dimensional automorphism group

The main theorem of this article is a characterization of non compact simply connected complete Kobayashi hyperbolic complex manifold of dimension n≽ 2 with real n ²-dimensional holomorphic automorphism group. Together with the earlier work [11, 12] and [13] of Isaev and Krantz, this yields a complete classification of the simply-connected, complete Kobayashi hyperbolic manifolds with dim_ℝ Aut (M) ≽ (dim_ℂ M)².     

一类有界对称域上的Hartogs型域的自同构群

本文研究了稍微广泛的一类Hartogs型域的自同构群.利用华域的自同构群,获得了一类有界对称域上的Hartogs型域的自同构群的具体形式,推广了有界对称域上的Hartogs型域的自同构群这一结果.     

Proper holomorphic self-maps of smooth bounded Reinhardt domains in C~n

It is proved that every proper holomorphic self-map of a smooth bounded Reinhardt domain of D'Angelo finite type in Cn (n > 1) is an automorphism.     

The Bergman Kernel Function and Full Group of Holomorphic Automorphism on a Reinhardt Domain

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Kodaira dimensions and hyperbolicity of nonpositively curved compact Kähler manifolds

In this article, we prove that a compact Kähler manifold M ⁿ with real analytic metric and with nonpositive sectional curvature must have its Kodaira dimension, its Ricci rank and the codimension of its Euclidean de Rham factor all equal to each other. In particular, M ⁿ is of general type if and only if it is without flat de Rham factor. By using a result of Lu and Yau, we also prove that for a compact Kähler surface M ² with nonpositive sectional curvature, if M ² is of general type, then it is Kobayashi hyperbolic.