Strict plurisubharmonicity of Bergman kernels on generalized annuli

作者：Wang Yanyan^*

来源：Annales Polonici Mathematici, 2014, 111(3): 237-243.

DOI：10.4064/ap111-3-2

• Bergman kernels
• plurisubharmonicity

Let A(zeta) = Omega - <(rho(zeta).Omega)over bar> be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel K-zeta(z) of A(zeta) is plurisubharmonic provided rho is an element of PSH(U). It is remarkable that A(zeta) is non-pseudoconvex when the dimension of A(zeta) is larger than one. For standard annuli in C, we obtain an interesting formula for partial derivative(2) log K-zeta/partial derivative zeta partial derivative(zeta) over bar, as well as its boundary behavior.

• 出版日期2014
• 单位同济大学