A generalized Hurwitz metric
Bull. Korean Math. Soc. 2020 Vol. 57, No. 5, 1127-1142
https://doi.org/10.4134/BKMS.b190789
Published online September 30, 2020
Arstu, Swadesh Kumar Sahoo
Simrol, Khandwa Road; Simrol, Khandwa Road
Abstract : In 2016, the Hurwitz metric was introduced by D. Minda in arbitrary proper subdomains of the complex plane and he proved that this metric coincides with the Poincar\'e's hyperbolic metric when the domains are simply connected. In this paper, we provide an alternate definition of the Hurwitz metric through which we could define a generalized Hurwitz metric in arbitrary subdomains of the complex plane. This paper mainly highlights various important properties of the Hurwitz metric and the generalized metric including the situations where they coincide with each other.
Keywords : Hyperbolic metric, Kobayashi metric, Hurwitz metric, Hurwitz covering, generalized Hurwitz metric, hyperbolic domain, Lipschitz domain
MSC numbers : Primary 30F45; Secondary 30C20, 30C80
Supported by : The research work of Arstu was supported by CSIR-UGC $($Grant No: 21/06/2015(i)EU-V$)$ and of S. K. Sahoo was supported by NBHM, DAE $($Grant No: $2/48 (12)/2016/${\rm NBHM (R.P.)/R \& D II}/$13613)$
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