Related papers: Examples of domains with non-compact automorphism …

We construct a class of bounded domains, on which the squeezing function is not uniformly bounded from below near a smooth and pseudoconvex boundary point.

We introduce the notion of domains with uniform squeezing property, study various analytic and geometric properties of such domains and show that they cover many interesting examples, including Teichmuller spaces and Hermitian symmetric…

The purpose of this article is twofold. The first aim is to characterize $h$-extendibility of smoothly bounded pseudoconvex domains in $\mathbb C^{n+1}$ by their noncompact automorphism groups. Our second goal is to show that if the…

Let $D=\{\rho<0\}$ be a smooth domain of finite type in an almost complex manifold (M,J) of real dimension four. We assume that the defining function $\rho$ is J-plurisubharmonic on a neighborhood of $\overline{D}$. We study the asymptotic…

A sufficient condition for the infinite dimensionality of the Bergman space of a pseudoconvex domain is given. This condition holds on any pseudoconvex domain that has at least one smooth boundary point of finite type in the sense of…

We study how the existence of a negatively pinched K\"ahler metric on a domain in complex Euclidean space restricts the geometry of its boundary. In particular, we show that if a convex domain admits a complete K\"ahler metric, with pinched…

In this paper we study domains in flag manifolds which are bounded in an affine chart and whose projective automorphism group acts co-compactly. In contrast to the many examples in real projective space, we will show that no examples exist…

The aim of this note is to explain a generalization to the real case of a well known result on the automorphism group of an unbounded tube type symmetric domain in a complex vector space of finite dimension.

In this paper we establish a gap theorem for the complex geometry of smoothly bounded convex domains which informally says that if the complex geometry near the boundary is close to the complex geometry of the unit ball, then the domain…

We shall explain here an idea to generalize classical complex analytic Kleinian group theory to any odd dimensional cases. For a certain class of discrete subgroups of $\PGL_{2n+1}(\C)$ acting on $\P^{2n+1}$, we can define their domains of…

We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension $n\ne 3$, whose group of holomorphic automorphisms has dimension $n^2+1$ and that, if a 3-dimensional connected hyperbolic complex manifold has…

Let $\Omega$ be a bounded, convex domain in a separable Hilbert space. The authors prove a version of the theorem of Bun Wong, which asserts that if such a domain admits an automorphism orbit accumulating at a strongly pseudoconvex boundary…

This paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in $\C^2$. We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the…

There exists a proper holomorphic mapping between balls of different dimensions such that it does not extend continuously to the boundary. The aim of this paper is to show the same phenomenon occurs for pseudoconvex domains of different…

In this paper we deal with the following question: is it true that any bounded smooth pseudoconvex domain in $\mathbb{C}^n$ whose boundary contains a $q$-dimensional complex manifold $M$ necessarily has a noncompact…

Bieberbach constructed in 1933 domains in $ \bf {C}^2$ which were biholomorphic to $ \bf {C}^2$ but not dense. The existence of such domains was unexpected. The special domains Bieberbach considered are basins of attraction of a cubic…

We show how to construct a class of smooth bounded pseudoconvex domains whose boundary contains a given Stein manifold with strongly pseudoconvex boundary, having a prescribed codimension and D'Angelo class (a cohomological invariant…

We treat the boundary problem for complex varieties with isolated singularities, of complex dimension greater than or equal to 3, non necessarily compact, which are contained in strongly convex, open subsets of a complex Hilbert space H. We…

The main result of this paper is that the identity component of the automorphism group of a compact, connected, strictly pseudoconvex CR manifold is compact unless the manifold is CR equivalent to the standard sphere. In dimensions greater…

The $\bar{\partial}$-Neumann operator (the inverse of the complex Laplacian) is shown to be noncompact on certain domains in complex Euclidean space. These domains are either higher-dimensional analogs of the Hartogs triangle, or have such…