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<p>We focus on the <i>d</i>-boundedness of the Bergman metric on a kind of quasi-homogeneous Hartogs domain without assuming the weight function to be plurisubharmonic. As corollaries, the Kähler hyperbolicity and a vanishing theorem can be obtained. Then we generalize these results to the high-dimensional case of the fiber of the Hartogs domain. Finally, we give a more explicit explanation for the condition of the weight function which is not plurisubharmonic but makes the Hartogs domain to be quasi-homogeneous.</p>

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The Kähler hyperbolicity on a kind of quasi-homogeneous domain

  • 期刊论文

  • 发表日期：

    2026年5月9日

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  • Mingming Chen,
  • An Wang,
  • Chengchen Zhong,
  • Xin Zhao

摘要

We focus on the d-boundedness of the Bergman metric on a kind of quasi-homogeneous Hartogs domain without assuming the weight function to be plurisubharmonic. As corollaries, the Kähler hyperbolicity and a vanishing theorem can be obtained. Then we generalize these results to the high-dimensional case of the fiber of the Hartogs domain. Finally, we give a more explicit explanation for the condition of the weight function which is not plurisubharmonic but makes the Hartogs domain to be quasi-homogeneous.