This analysis reveals a unique constant for K"ahler-hyperbolicity, indicating the relationship between rank and genus.
In this paper, we characterize the K\"ahler-hyperbolicity length of a bounded symmetric domain, defined by its rank and genus, as a unique constant determined by a constant gradient length of a special Bergman potential. Additionally, we establish a characterization of the lower bound of L^∞ norm of the gradient length of any Bergman potential.
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Choi et al. (2025) studied this question.
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