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Science China Mathematics 2005年第Z1期48卷 225-237页

作者： guy roos Nevski Prospekt 113/4-53 191024 St Petersburg Russian Federation

We introduce the notion of virtual Bergman kernel and study some of its applications.

关键词： Bergman kernel, weighted Bergman kernel, virtual Bergman kernel.

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New classes of domains with explicit Bergman kernel

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Science China Mathematics 2004年第3期47卷 352-371页

作者： roos guy Henan University Kaifeng 475001 China Nevski Prospekt 113/4-53 191024 St Petersburg Russian Federation

We introduce two classes of egg type domains, built on general boundedsymmetric domains, for which we obtain the Bergman kernel inexplicit formulas. As an auxiliary tool, we compute the integralof complex powers of the generic norm on a bounded symmetricdomains using the well-known integral of Selberg. Thisgeneralizes matrix integrals of Hua and leads to a specialpolynomial with integer or half-integer coefficients attached toeach irreducible bounded symmetric domain.

关键词： Cartan domain, Bergman kernel, holomorphic automorphism group, boundedsymmetric domain, Hua integral.

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The Khler-Einstein metric for some Hartogs domains over symmetric domains

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Science China Mathematics 2006年第9期 1175-1210页

作者： roos guy Nevski Prospekt 113/4-53 191024 St Petersburg Russian Federation

We study the complete Kahler-Einstein metric of a Hartogs domainΩbuilt on an irreducible bounded symmetric domainΩ, using a power Nμof the generic norm ofΩ.The generating function of the Kahler-Einstein metric satisfies a complex Monge-Ampere equation with a boundary condition. The domainΩis in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X∈[0,1[. This allows us to reduce the Monge-Ampere equation to an ordinary differential equation with a limit condition. This equation can be explicitly solved for a special valueμ0 ofμ.. We work out the details for the two exceptional symmetric domains. The special valueμ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains.

关键词： Hartogs domain K(a|¨)hler-Einstein metric bounded symmetric domain

Cartan-Hartogs域的Khler-Einstein度量

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中国科学（A辑） 2006年第11期36卷 1201-1233页

作者：王安殷慰萍张利友 roos guy 首都师范大学数学科学学院 Nevski prospekt 113/4-53 191024 St PetersburgRussian Federation

研究以不可约有界对称域Ω为底空间的一类Hartogs域(?)上的K(?)hler- Einstein度量,这种域称之为Cartan-Hartogs域,是华罗庚域的一种,其中K(?)hler- Einstein度量的生成函数满足一带有边界条件的复Monge-Ampère方程．一般地,域(?)是非... 详细信息

研究以不可约有界对称域Ω为底空间的一类Hartogs域(?)上的K(?)hler- Einstein度量,这种域称之为Cartan-Hartogs域,是华罗庚域的一种,其中K(?)hler- Einstein度量的生成函数满足一带有边界条件的复Monge-Ampère方程．一般地,域(?)是非齐性域,其上有一全纯自同构子群以及群不变轨道X∈[0,1[,因此可以把复Monge-Ampère方程化为常微分方程,并且此方程在临界值μ_0=μ时能够显式解出．临界值μ_0对于研究其他不变度量如Bergman度量也是非常有意义的．文中还给出一个猜想,并且证明了该猜想对于两类两类例外域是成立的．

关键词： Hartogs域 Kfihler—Einstein度量有界对称域例外域 Cartan—Hartogs域

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