Strict plurisubharmonicity of Bergman kernels on generalized annuli

Yanyan Wang. "Strict plurisubharmonicity of Bergman kernels on generalized annuli." Annales Polonici Mathematici 111.3 (2014): 237-243. <http://eudml.org/doc/280420>.

@article{YanyanWang2014,
abstract = {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.},
author = {Yanyan Wang},
journal = {Annales Polonici Mathematici},
keywords = {Bergman kernel; plurisubharmonicity},
language = {eng},
number = {3},
pages = {237-243},
title = {Strict plurisubharmonicity of Bergman kernels on generalized annuli},
url = {http://eudml.org/doc/280420},
volume = {111},
year = {2014},
}

TY - JOUR
AU - Yanyan Wang
TI - Strict plurisubharmonicity of Bergman kernels on generalized annuli
JO - Annales Polonici Mathematici
PY - 2014
VL - 111
IS - 3
SP - 237
EP - 243
AB - 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.
LA - eng
KW - Bergman kernel; plurisubharmonicity
UR - http://eudml.org/doc/280420
ER -