Abstract
Jorgenson and Kramer (Compos Math 142:679–700, 2006) proved a certain key identity which relates the two natural metrics, namely the hyperbolic metric and the canonical metric defined on a compact hyperbolic Riemann surface. In this article, we extend this identity to noncompact hyperbolic Riemann orbisurfaces of finite volume, which can be realized as a quotient space of the action of a Fuchsian subgroup of first kind on the hyperbolic upper half plane. Our result can be seen as an extension of the key identity to elliptic fixed points and cusps at the level of currents.
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