On free holomorphic C-actions on Cn and homogeneous Stein manifolds.
On holomorphically separable complex solv-manifolds
Let be a solvable complex Lie group and a closed complex subgroup of . If the global holomorphic functions of the complex manifold locally separate points on , then is a Stein manifold. Moreover there is a subgroup of finite index in with nilpotent. In special situations (e.g. if is discrete) normalizes and is abelian.
On horospheres and holomorphic endomorfisms of the Siegel disc
On invariant domains in certain complex homogeneous spaces
Given a compact connected Lie group . For a relatively compact -invariant domain in a Stein -homogeneous space, we prove that the automorphism group of is compact and if is semisimple, a proper holomorphic self mapping of is biholomorphic.
On invariant domains of holomorphy
On Lie algebra decompositions, related to spherical homogeneous spaces.
On local CR-transformations of Levi-degenerate group orbits in compact Hermitian symmetric spaces
We present a large class of homogeneous 2-nondegenerate CR-manifolds , both of hypersurface type and of arbitrarily high CR-codimension, with the following property: Every CR-equivalence between domains , in extends to a global real-analytic CR-automorphism of . We show that this class contains -orbits in Hermitian symmetric spaces of compact type, where is a real form of the complex Lie group and has an open orbit that is a bounded symmetric domain of tube type.
On Locally Symmetrie Homogeneous Domains of Completely Reducible Linear Lie Groups.
On Non-Compact Complex Nil-Manifolds.
On Penney's Cayley transform of a homogeneous Siegel domain.
On proper R-actions on hyperbolic Stein surfaces.
On roots of the automorphism group of a circular domain in
We study the properties of the group Aut(D) of all biholomorphic transformations of a bounded circular domain D in containing the origin. We characterize the set of all possible roots for the Lie algebra of Aut(D). There exists an n-element set P such that any root is of the form α or -α or α-β for suitable α,β ∈ P.
On Stein extensions of real symmetric spaces.
On tameness and growth conditions.
On the automorphism group of a complex sphere.
On the Automorphism Group of a Stein Manifold.
On the automorphism group of strongly pseudoconvex domains in almost complex manifolds
In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost...
On the automorphism groups of algebraic bounded domains.
On the automorphism groups of convex domains in .
On the automorphisms of the spectral unit ball
Let Ω be the spectral unit ball of Mₙ(ℂ), that is, the set of n × n matrices with spectral radius less than 1. We are interested in classifying the automorphisms of Ω. We know that it is enough to consider the normalized automorphisms of Ω, that is, the automorphisms F satisfying F(0) = 0 and F'(0) = I, where I is the identity map on Mₙ(ℂ). The known normalized automorphisms are conjugations. Is every normalized automorphism a conjugation? We show that locally, in a neighborhood of a matrix with...