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Carathéodory Density of the Hurwitz Metric on Plane Domains

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Abstract

It is well known that the Carathéodory metric is a natural generalization of the Poincaré metric, namely, the hyperbolic metric of the unit disk. 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 hyperbolic metric when the domains are simply connected. In this paper, we define a new metric which generalizes the Hurwitz metric in the sense of Carathéodory. Our main focus is to study its various basic properties in connection with the Hurwitz metric.

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Acknowledgements

The authors would like to thank the referee for his/her careful reading of the manuscript and useful remarks. The research work of Arstu is supported by CSIR-UGC (Grant No: 21/06/2015(i)EU-V) and of S. K. Sahoo is partially supported by NBHM, DAE (Grant No: 2/48 (12)/2016/NBHM (R.P.)/R & D II/13613).

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Authors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa Road, Indore, 453 552, India

    Arstu & Swadesh Kumar Sahoo

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  1. Arstu
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  2. Swadesh Kumar Sahoo
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Correspondence to Swadesh Kumar Sahoo.

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Communicated by V. Ravichandran.

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Arstu, Sahoo, S.K. Carathéodory Density of the Hurwitz Metric on Plane Domains. Bull. Malays. Math. Sci. Soc. 43, 4457–4467 (2020). https://doi.org/10.1007/s40840-020-00937-4

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  • DOI: https://doi.org/10.1007/s40840-020-00937-4

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