Abstract
The Hurwitz metric was recently defined by Minda by considering a variational problem that involves holomorphic maps from the disc that are globally injective at the origin. In this note, sharp boundary estimates for this metric are obtained on $C^2$-smooth planar domains and as a consequence, it is shown that it is uniformly comparable with the Carathéodory and Kobayashi metrics on such domains. In addition, estimates for the generalized curvatures of this metric are also given.
Citation
Amar Deep Sarkar. Kaushal Verma. "On the Hurwitz metric." Kodai Math. J. 44 (1) 126 - 136, March 2021. https://doi.org/10.2996/kmj44108
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