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- W2950768869 abstract "An explicit formula for the generalized hyperbolic metric on the thrice--punctured sphere $P backslash {z_1, z_2, z_3}$ with singularities of order $alpha_j le 1$ at $z_j$ is obtained in all possible cases $alpha_1+alpha_2+alpha_3 >2$. The existence and uniqueness of such a metric was proved long time ago by Picard cite{Pic1905} and Heins cite{Hei62}, while explicit formulas for the cases $alpha_1=alpha_2=1$ were given earlier by Agard cite{AG} and recently by Anderson, Sugawa, Vamanamurthy and Vuorinen cite{A}. We also establish precise and explicit lower bounds for the generalized hyperbolic metric. This extends work of Hempel cite{Hem79} and Minda cite{Min87b}. As applications, sharp versions of Landau-- and Schottky--type theorems for meromorphic functions are obtained." @default.
- W2950768869 created "2019-06-27" @default.
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- W2950768869 date "2009-11-04" @default.
- W2950768869 modified "2023-09-27" @default.
- W2950768869 title "Metrics with conical singularities on the sphere and sharp extensions of the theorems of Landau and Schottky" @default.
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