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On the complex geometry of invariant domains in complexified symmetric spaces

Karl-Hermann Neeb (1999)

Annales de l'institut Fourier

Let $M = G / H$ be a real symmetric space and $𝔤 = 𝔥 + 𝔮$ the corresponding decomposition of the Lie algebra. To each open $H$ -invariant domain $D_{𝔮} \subseteq i 𝔮$ consisting of real ad-diagonalizable elements, we associate a complex manifold $Ξ (D_{𝔮})$ which is a curved analog of a tube domain with base $D_{𝔮}$ , and we have a natural action of $G$ by holomorphic mappings. We show that $Ξ (D_{𝔮})$ is a Stein manifold if and only if $D_{𝔮}$ is convex, that the envelope of holomorphy is schlicht and that $G$ -invariant plurisubharmonic functions correspond to convex $H$ -invariant...

On the existence of parabolic actions in convex domains of $ℂ^{k + 1}$

François Berteloot, Ninh Van Thu (2015)

Czechoslovak Mathematical Journal

We prove that the one-parameter group of holomorphic automorphisms induced on a strictly geometrically bounded domain by a biholomorphism with a model domain is parabolic. This result is related to the Greene-Krantz conjecture and more generally to the classification of domains having a non compact automorphisms group. The proof relies on elementary estimates on the Kobayashi pseudo-metric.

On the fundamental group of the fixed points of an unipotent action.

Daniel Gross (1988)

Manuscripta mathematica

On the group of holomorphic automorphisms of Cn.

László Lempert, Erik Andersén (1992)

Inventiones mathematicae

On the holomorphic separabilitiy of discrete quotients of complex Lie groups.

Karl Oeljeklaus (1992)

Mathematische Zeitschrift

On the order of the automorphism group of a surface of general type.

A.T. Huckleberry, M. Sauer (1990)

Mathematische Zeitschrift

On the Rigidity of Certain Discrete Groups and Algebraic Varieties.

J. Jost, S.T. Yau (1987)

Mathematische Annalen

On the Torelli problem of Abelian complex Lie groups.

Erich Selder (1988)

Mathematica Scandinavica

On weighted Bergman kernels of bounded domains

Sorin Dragomir (1994)

Studia Mathematica

We build on work by Z. Pasternak-Winiarski [PW2], and study a-Bergman kernels of bounded domains $Ω \subset ℂ^{N}$ for admissible weights $a \in L ¹ (Ω)$ .

Optimal destabilizing vectors in some Gauge theoretical moduli problems

Laurent Bruasse (2006)

Annales de l’institut Fourier

We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing $1$ -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...

Displaying 21 – 30 of 30

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