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<p>We describe a method of defining a Hermitian metric on Kobayashi hyperbolic manifolds. The metric is distance decreasing under holomorphic mappings, up to a multiplicative constant. This method is distinct from the classical construction of Wu and yields a metric which is expected to have superior regularity properties.</p>

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A Hermitian metric on hyperbolic complex manifolds

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Debraj Chakrabarti,
  • Prachi Mahajan

摘要

We describe a method of defining a Hermitian metric on Kobayashi hyperbolic manifolds. The metric is distance decreasing under holomorphic mappings, up to a multiplicative constant. This method is distinct from the classical construction of Wu and yields a metric which is expected to have superior regularity properties.