Geodesic
Injectivity criteria for some domains.~I
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 104-124

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New conditions are given for continuously differentiable mappings of some plane domains to be injective. In the case of plane circular domain these criteria coincide with well-known conditions. The method of locally homeomorphic extension is used. 
@article{ZNSL_1998_255_a6,
     author = {E. L. Patsevich},
     title = {Injectivity criteria for some {domains.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {104--124},
     publisher = {mathdoc},
     volume = {255},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a6/}
}
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E. L. Patsevich. Injectivity criteria for some domains.~I. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 104-124. http://geodesic.mathdoc.fr/item/ZNSL_1998_255_a6/