ON A THEOREM OF NEHARI AND QUASIDISCS
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by Scientiarum Fennicae, Series A. I. Mathematica, Martin Chuaqui
ftp://ftp.maths.tcd.ie/pub/EMIS/journals/AASF/Vol18/chuaqui.ps.gz
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Abstract:
Abstract. Let f be a locally injective analytic map of the unit disc D and let ff; zg be its Schwarzian derivative. Suppose jff; zgj 2p(jzj). We use the classical connection between Schwarzian derivative and second order linear equations to show that, for a particular class of functions p, the image f(D) is a quasidisc. The analysis centers on the differential equation y
Citations
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| 29 | Univalent functions and Teichmuller spaces – Lehto - 1987 |
| 13 | Ordinary Differential Equations in the Complex Domain – Hille - 1976 |
| 8 | The Schwarzian derivative and schlicht functions – Nehari - 1949 |
| 4 | On the Nehari univalence criterion and quasicircles – Gehring, Pommerenke - 1984 |
| 2 | Sharp distortion theorems associated with the Schwarzian derivative – Chuaqui, Osgood - 1993 |
| 2 | Univalence criteria depending on the Schwarzian derivative – Nehari - 1979 |
| 1 | Positive superharmonic functions and the Holder continuity of conformal mappings – Anderson, Hinkkanen - 1989 |
