We consider the subharmonicity property of the logarithm of Azukawa pseudometrics of pseudoconvex domains under pseudoconvex variations. We prove that such a property holds for the variation of balanced domains. We also give a non-balanced example. The relation of the volume of Azukawa indicatrix and the estimate in the Ohsawa–Takegoshi L2-extension theorem is also discussed.

中文翻译：

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平衡域的 Azukawa 伪度量的次谐波变化

我们考虑在伪凸变化下伪凸域的Azukawa伪度量的对数的次谐波性质。我们证明了这种性质适用于平衡域的变化。我们还举了一个不平衡的例子。大泽竹越中小津指标体积与估计的关系大号2-扩展定理也被讨论。