Invariant Plurisubharmonic Functions and Hypersurfaces on Semisimple Complex Lie Groups.
Le problème de Lévi pour les espaces homogènes
Levi-Curvature of Manifolds with a Stein Rational Fibration.
Lie group structures and reproducing kernels on the unit ball of
Si introducono due strutture di gruppo di Lie su un dominio di Siegel omogeneo di . Per la palla unitaria si definisce una famiglia ad un parametro di strutture intermedie; ad ognuna di esse viene associato naturalmente un nucleo riproducente ottenendo un'interpolazione tra il nucleo di Bergman ed il nucleo di Szego.
Links of surface singularities and CR space forms.
Multiplicity-free complex manifolds.
Naive boundary strata and nilpotent orbits
We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Nef value of homogeneous line bundles and related vanishing theorems.
Oka manifolds: From Oka to Stein and back
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...
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 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 Locally Symmetrie Homogeneous Domains of Completely Reducible Linear Lie Groups.
On Non-Compact Complex Nil-Manifolds.
On tameness and growth conditions.
On the holomorphic separabilitiy of discrete quotients of complex Lie groups.
On the Kobayashi and Caratheodory pseudometric reductions of homogeneous complex spaces
Orbifold-Uniformizing Differential Equations.
Peirce-Zerlegungen und Jordan-Strukturen zu homogenen Kegeln.
Pluriharmonic functions on symmetric tube domains with BMO boundary values
Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.