具有非紧连通自同构群的CR流形

On the automorphism groups of models in $\mathbb C^2$

In this note, we consider models in $\mathbb C^2$. The purpose of this note is twofold. We first show a characterization of models in $\mathbb C^2$ by their noncompact automorphism groups. Then we give an explicit description for automorphism groups of models in $\mathbb C^2$.

On a Theorem of Bers, with Applications to the Study of Automorphism Groups of Domains

We study and generalize a classical theorem of L. Bers that classifies domains up to biholomorphic equivalence in terms of the algebras of holomorphic functions on those domains. Then we develop applications of these results to the study of domains with noncompact automorphism group.

Complete hyperbolic Stein manifolds with prescribed automorphism groups

It is well-known that the automorphism group of a hyperbolic manifold is a Lie group.Conversely, it is interesting to see whether or not any Lie group could be prescribed asthe automorphism group of certain complex manifold. Whenthe Lie group $G$ is compact and connected, this problem has been completelysolved by Bedford-Dadok and independently by Saerens-Zame on 1987. Theyhave constructed \spc bounded domains $Ω$ such that $Aut(Ω)=G$. For Bedford-Dadok's $Ω, 0\le dim_{\Bbb C}Ω- dim_{\Bbb R}G\le 1$; for generic Saerens-Zame's$Ω,dim_{\Bbb C}Ω\gg dim_{\Bbb R}G$.J. Winkelmann has answered affirma…

Realizing Connected Lie Groups As Automorphism Groups Of Complex Manifolds

We show that every connected real Lie group can be realized as the full automorphism group of a Stein hyperbolic complex manifold.

将半单李群实现为有界域的全纯自同构群

Realizing semisimple Lie groups as holomorphic automorphism groups of bounded domains

本文证明了包括所有连通实半单群在内的一大类李群（含许多非线性李群）均可实现为仿射复空间有界域的全纯自同构群，推广了1990年关于连通线性李群的结论。

Characterization of ${\bf C}^n$ by its automorphism group

We show that if the group of holomorphic automorphisms of a connected Stein manifold $M$ is isomorphic to that of ${\bf C}^n$ as a topological group equipped with the compact-open topology, then $M$ is biholomorphically equivalent to ${\bf C}^n$.

On a domain in C^2 with generic piecewise smooth Levi-flat boundary and non-compact automorphism group

In this paper, we prove that if D is a simply-connected domain in C^2 with generic piecewise smooth Levi-flat boundary and non-compact automorphism group, then D is biholomorphic to the bidisc. The proof is based on a careful analysis of invariant measures.

On the group of holomorphic automorphisms of model surfaces

It is proved that the group of holomorphic automorphisms of holomorphically homogeneous nondegenerate (finite Bloom-Graham type + holomorphic nondegenaracy) model surface Q is a subgroup of the group of birational automorphisms of the ambient space (Cremona group) with uniformly bounded degree. An estimate of the degree of the automorphisms in terms of the dimension of the ambient space is given (Theorem 4). It is proved that none of the conditions of the theorem can be omitted. We consider also the question about connectedness of the automorphism group of Q (Theorem 7).

对称双圆盘上的等距映射，II

Isometries in the symmetrized bidisc, II

该研究证明了保持Kobayashi距离的从单位圆盘D到对称双圆盘G₂的映射f必为全纯或反全纯，完善了对称双圆盘上等距映射的相关理论。

容许紧的全纯自同构可迁群的紧连通复流形

Compact, connected, complex manifolds that admit a compact transitive group of holomorphic automorphisms

本文提出一种仅基于李理论标准结论的李代数方法，为紧复齐性流形相关经典结论给出新证明，还提供了将典范阿贝尔李代数与紧李代数上可积复结构关联的方式，拓展了前人研究。

Homogeneous Kobayashi-hyperbolic manifolds with high-dimensional group of holomorphic automorphisms

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 2$ whose holomorphic automorphism group has dimension $n^2-2$. This result complements an existing classification for automorphism group dimension $n^2-1$ and greater obtained without the homogeneity assumption.

The automorphism group and limit set of a bounded domain II: the convex case

For convex domains with $C^{1,ε}$ boundary we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different closed complex faces of the boundary, then the automorphism group has finitely many components and the connected component of the identity is the almost direct product of a compact group and a non-compact connected simple Lie group with real rank one and finite center. In this case, we also show the limit set is homeomorphic to a sphere and prove a gap theorem: either the domain is biholomorphic to the unit ball (and the…

Homogeneous Kobayashi-hyperbolic manifolds with automorphism group of subcritical dimension

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 2$ whose holomorphic automorphism group has dimension $n^2-3$. This result complements existing classifications for automorphism group dimension $n^2-2$ (which is in some sense critical) and greater.

Sur les remplissages holomorphes équivariants

A complex filling of a CR manifold is said to be equivariant with respect to a CR action if the action extends to a smooth action by biholomorphisms on the whole filling. Under a noncompactness condition for the action, we describe all equivariant fillings of strongly pseudoconvex CR manifolds of dimension 3. Since the standard sphere is the only compact strongly pseudoconvex CR manifold whose automorphism group is not compact, we only have to study its fillings.

Further steps towards classifying homogeneous Kobayashi-hyperbolic manifolds with high-dimensional automorphism group

We determine all connected homogeneous Kobayashi-hyperbolic manifolds of dimension $n\ge 4$ whose group of holomorphic automorphisms has dimension either $n^2-4$, or $n^2-5$, or $n^2-6$. This paper continues a series of articles that achieve classifications for automorphism group dimension $n^2-3$ and greater.

On automorphisms of blowups of $\mathbb{P}^3$

Let $π:X\rightarrow \mathbb{P}^3$ be a finite composition of blowups along smooth centers. We show that for "almost all" of such $X$, if $f\in Aut(X)$ then its first and second dynamical degrees are the same. We also construct many examples of finite blowups $X\rightarrow \mathbb{P}^3$, whose automorphism group $Aut(X)$ has only finitely many connected components. We also present a heuristic argument showing that for a "generic" compact Kähler manifold $X$ of dimension $\geq 3$, the automorphism group $Aut(X)$ has only finitely many connected components.

The Jordan property for Lie groups and automorphism groups of complex spaces

We prove that the family of all connected n-dimensional real Lie groups is uniformly Jordan for every n. This implies that all algebraic groups (not necessarily affine) over fields of characteristic zero and some transformation groups of complex spaces and Riemannian manifods are Jordan.