A Hermitian metric on hyperbolic complex manifolds
Complex Variables
2025-05-22 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2505.15780,
title = {A Hermitian metric on hyperbolic complex manifolds},
author = {Debraj Chakrabarti and Prachi Mahajan},
journal= {arXiv preprint arXiv:2505.15780},
year = {2025}
}