Abstract
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. Bibliography: 18 titles.
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 237, 1997, pp. 148–160.
This research was partially supported by the Russian Foundation for Basic Research, grant 97-01-00259.
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Solynin, A.Y. Radial projection and the poincaré metric. J Math Sci 95, 2267–2275 (1999). https://doi.org/10.1007/BF02172471
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DOI: https://doi.org/10.1007/BF02172471