A generalized Hurwitz metric
Complex Variables
2020-03-30 v1
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.
Cite
@article{arxiv.2003.12335,
title = {A generalized Hurwitz metric},
author = {Arstu and Swadesh Kumar Sahoo},
journal= {arXiv preprint arXiv:2003.12335},
year = {2020}
}
Comments
16 pages, To appear in the Bull. Korean Math. Soc