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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.
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참고문헌 (9)
참고문헌 신청
D. Burago / 2001 / A course in metric geometry / American Mathematical Society
Kyong T. Hahn / 1981 / Some remarks on a new pseudo-differential metric / Annales Polonici Mathematici 39(1):71~81
A. Hurwitz / 1904 / Uher die Anwendung der elliptischen Modulfunktionen auf einen Satz der allgemeinen, Funktionentheorie / Vierteljahrschr. Naturforsch. Gesell. Zurich 49:242~253
L. Keen / 2007 / In the tradition of Ahlfors-Bers. IV / Amer. Math. Soc :107~118
L. Keen / 2007 / Hyperbolic geometry from a local viewpoint / Cambridge University Press
Kyong T. Hahn / 1981 / Some remarks on a new pseudo-differential metric / Annales Polonici Mathematici 39(1):71~81
A. Hurwitz / 1904 / Uher die Anwendung der elliptischen Modulfunktionen auf einen Satz der allgemeinen, Funktionentheorie / Vierteljahrschr. Naturforsch. Gesell. Zurich 49:242~253
L. Keen / 2007 / In the tradition of Ahlfors-Bers. IV / Amer. Math. Soc :107~118
L. Keen / 2007 / Hyperbolic geometry from a local viewpoint / Cambridge University Press
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