Geodesic
Quasiconformal reflection for generalized spiral domains
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 185-198

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We discuss a method of constructing a generalized spiral domain such that the quasiconformal reflection on the boundary of this domain can be described explicitly. 
@article{ZNSL_1999_262_a8,
     author = {E. L. Patsevich},
     title = {Quasiconformal reflection for generalized spiral domains},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {185--198},
     publisher = {mathdoc},
     volume = {262},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a8/}
}
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E. L. Patsevich. Quasiconformal reflection for generalized spiral domains. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 27, Tome 262 (1999), pp. 185-198. http://geodesic.mathdoc.fr/item/ZNSL_1999_262_a8/