Geodesic
Injectivity criteria for some domains.~II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 125-139

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New sufficient conditions are found for continuously differentiable mappings in some plane domains to be injective. This result is obtained by using the locally homeomorphic extension method. New univalence criteria for meromorphic functions are given by means of the quasiconformal extension method. These criteria are stated in terms of the coefficients of a differential equation related to the Schwarzian derivative of the function under consideration. 
@article{ZNSL_1998_255_a7,
     author = {E. L. Patsevich},
     title = {Injectivity criteria for some {domains.~II}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--139},
     publisher = {mathdoc},
     volume = {255},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a7/}
}
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E. L. Patsevich. Injectivity criteria for some domains.~II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 125-139. http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a7/