Exceptional symmetric domains

Quasi-exceptional domains

Exceptional domains are domains on which there exists a positive harmonic function, zero on the boundary and such that the normal derivative on the boundary is constant. Recent results classify exceptional domains as belonging to either a certain one-parameter family of simply periodic domains or one of its scaling limits. We introduce quasi-exceptional domains by allowing the boundary values to be different constants on each boundary component. This relaxed definition retains the interesting property of being an \emph{arclength quadrature domain}, and also preserves the connection to the holl…

Holomorphic isometries from the unit ball into symmetric domains

We construct isometric holomorphic embeddings of the unit ball into higher rank symmetric domains, first discovered by Mok, in an explicit way using Jordan triple systems, and prove uniqueness results for all domains, including the exceptional domains of dimension 16 and 27.

Compact Composition Operators on the Bloch Space in Bounded Symmetric Domains

Let $Ω$ be a bounded symmetric domain except the two exceptional domains of ${\Bbb C}^N$ and $ϕ$ a holomorphic self-map of $Ω.$ This paper gives a sufficient and necessary condition for the composition operator $C_ϕ$ induced by $ϕ$ to be compact on the Bloch space $β(Ω)$.

The Kaehler-Einstein metric for some Hartogs domains over bounded symmetric domains

We study the complete Kähler-Einstein metric of a Hartogs domain $\widetilde Ω$, which is obtained by inflation of an irreducible bounded symmetric domain $Ω$, using a power $N^μ$ of the generic norm of $Ω$. The generating function of the Kähler-Einstein metric satisfies a complex Monge-Ampère equation with boundary condition. The domain $\widetilde Ω$ is in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by $X\in\lbrack0,1[$. This allows to reduce the Monge-Ampère equation to an ordinary differential equation with limit condition. This eq…

线丛Shilov--Poisson变换在有界对称域上的边界刚性

Boundary Rigidity of Line-Bundle Shilov--Poisson Transforms on Bounded Symmetric Domains

研究有界对称域上线丛Shilov--Poisson变换的边界刚性，确定有限正则性在内部强制为零或满足协变微分方程，并给出Graham型定理。

The exceptional set and the Green-Griffiths locus do not always coincide

We give a very simple criterion in order to ensure that the Green-Griffiths locus of a projective manifold is the whole manifold. Next, we use it to show that the Green-Griffiths locus of any projective manifold uniformized by a bounded symmetric domain of rank greater than one is the whole manifold. In particular, this clarifies an old example given by M. Green to S. Lang.