Plurisubharmonicity of Bergman Kernels on generalized annuli

2013/12/10 by Wang, Yanyan
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1312.2689

Abstract

Let A_ζ=Ω-ρ(ζ)⋅Ω be a family of generalized annuli over a domain U. We show that the logarithm log K_ζ(z) 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 \mathbb C, we obtain an interesting formula for ∂² log K_ζ/∂ ζ∂ζ, as well as its boundary behavior.

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