Strict plurisubharmonicity of Bergman kernels on generalized annuli

• Autorzy: Yanyan Wang
• Języki publikacji: EN

Abstrakty

EN

Let $A_ζ = Ω - \overline{ρ(ζ)·Ω}$ be a family of generalized annuli over a domain U. We show that the logarithm of the Bergman kernel $K_{ζ}(z)$ of $A_ζ$ is plurisubharmonic provided ρ ∈ PSH(U). It is remarkable that $A_ζ$ is non-pseudoconvex when the dimension of $A_ζ$ is larger than one. For standard annuli in ℂ, we obtain an interesting formula for $∂²log K_{ζ}/∂ζ∂ζ̅$, as well as its boundary behavior.

Kategorie tematyczne

• 32A25: Integral representations; canonical kernels (Szeg\H o, Bergman, etc.)
• 32U05: Plurisubharmonic functions and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2014
• Tom: 111
• Numer: 3
• Strony: 237-243

Daty

wydano

2014

Twórcy

autor

Yanyan Wang

• Department of Mathematics, Tongji University, 200092 Shanghai, China

Identyfikatory

DOI

10.4064/ap111-3-2