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

We give an example of a bounded, pseudoconvex, circular domain in ${\mathbb C}^3$ with smooth, real-analytic boundary and non-compact automorphism group, which is not biholomorphically equivalent to any Reinhardt domain.

We give an explicit description of smoothly bounded Reinhardt domains with noncompact automorphism groups. In particular, this description confirms a special case of a conjecture of Greene/Krantz.

We give a complete description of bounded Reinhardt domains of finite boundary smoothness that have non-compact automorphism group. As part of this program, we show that the classification of domains with non-compact automorphism group and…

We survey results arising from the study of domains in C^n with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even…

Let $D$ be a bounded domain in $\mathbf C^2$ with a non-compact group of holomorphic automorphisms. Model domains for $D$ are obtained under the hypothesis that at least one orbit accumulates at a boundary point near which the boundary is…

Let $X$ be an arbitrary complex surface and $D \subset X$ a domain that has a non compact group of holomorphic automorphisms. A characterization of those domains $D$ that admit a smooth real analytic, finite type boundary orbit accumulation…

For convex domains with $C^{1,\epsilon}$ 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…

In this paper we study the automorphism group of smoothly bounded convex domains. We show that such a domain is biholomorphic to a "polynomial ellipsoid" (that is, a domain defined by a weighted homogeneous balanced polynomial) if and only…

We construct several new examples of homogeneous domains in complex space that do not have bounded realisations. They are equivalent to tubes over affinely homogeneous domains in real space and have a real-analytic everywhere Levi…

For bounded pseudoconvex domains with finite type we give a precise description of the automorphism group: if an orbit of the automorphism group accumulates on at least two different points of the boundary, then the automorphism group has…

We study some special almost complex structures on strictly pseudoconvex domains. They appear naturally as limits under a nonisotroping scaling procedure and play a role of model objects in the geometry of almost complex manifolds with…

We give an explicit description of hyperbolic Reinhardt domains D in C^2 such that: (i) D has C^k-smooth boundary for some k greater than or equal to 1, (ii) D intersects at least one of the coordinate complex lines $\{z_1=0\}$,…

The Diederich-Forn{\ae}ss worm domain, an important example of a smoothly bounded pseudoconvex domain without a Stein neighborhood basis, provides key counterexamples in the theory of Several Complex Variables. In this paper, we examine its…

We study the semicontinuity of automorphism groups for perturbations of domains in complex space or in complex manifolds. We provide a new approach to the study of such results for domains having minimal boundary smoothness. The emphasis in…

We study domains in complex $n$-space with automorphism group that does not depend on the full $n$ dimensions of the ambient space. A sufficient geometric condition is obtained to guarantee that a domain has such a "thin" automorphism…

By considering intrinsic geometric conditions, we introduce a new class of domains in complex Euclidean space. This class is invariant under biholomorphism and includes strongly pseudoconvex domains, finite type domains in dimension two,…

Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in $\CC^n$, $n > 1$, with Lipschitz boundary, but it…

We show that the symmetrized bidisc is a $\Bbb C$-convex domain. This provides an example of a bounded $\Bbb C$-convex domain which cannot be exhausted by domains biholomorphic to convex domains.

We explicitly compute the Dolbeault cohomologies of certain domains in complex space generalizing the classical Hartogs figure. The cohomology groups are non-Hausdorff topological vector spaces, and it is possible to identify the reduced…

We first show that for a bounded pseudoconvex domain with a manifold quotient of finite-volume in the sense of Kahler-Einstein measure, the identity component of the automorphism group of this domain is semi-simple without compact factors.…