Abstract
In the unit disk D = {z ∈ ℂ ∣z∣ < 1}, the Poincaré metric ∣dz∣/(1 —∣z∣2) plays quite an important role in modern function theory. Various generalizations of this metric to Riemann surfaces have been given, e.g., hyperbolic (Kobayashi) metric, Carathéodory metric, Hahn metric, Begman metric and so on. In this article, we will provide a unifying treatment of such invariant metrics and explain a general principle dominating those metrics by some universal metrics.
The author was partially supported by the Ministry of Education, Grant-in-Aid for Encouragement of Young Scientists, 11740088.
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© 2000 Kluwer Academic Publishers
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Sugawa, T. (2000). Unified Approach to Conformally Invariant Metrics on Riemann Surfaces. In: Begehr, H.G.W., Gilbert, R.P., Kajiwara, J. (eds) Proceedings of the Second ISAAC Congress. International Society for Analysis, Applications and Computation, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0271-1_35
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DOI: https://doi.org/10.1007/978-1-4613-0271-1_35
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