A generalized Hurwitz metric
Bull. Korean Math. Soc.
Published online July 10, 2020
Arstu and Swadesh Kumar Sahoo
Indian Institute of Technology Indore
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 : 30F45, 30C20
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