This approach describes a distinct Hermitian metric for Kobayashi hyperbolic manifolds, suggesting improved regularity properties.
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.
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Chakrabarti et al. (2025) studied this question.
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