Geodesic
Radial projection and the Poincar\'e metric
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 148-160

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Some estimates for the Poincaré metric of a planar domain are obtained in terms of the radial projection of the complement of the domain onto the unit circle. These estimates allow us, in particular, to strengthen the well-known Lavrent'ev theorem on the product of conformal radii of nonoverlapping domains. The proofs use the polarization transformation. 
@article{ZNSL_1997_237_a11,
     author = {A. Yu. Solynin},
     title = {Radial projection and the {Poincar\'e} metric},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {148--160},
     publisher = {mathdoc},
     volume = {237},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a11/}
}
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A. Yu. Solynin. Radial projection and the Poincar\'e metric. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 14, Tome 237 (1997), pp. 148-160. http://geodesic.mathdoc.fr/item/ZNSL_1997_237_a11/