Geodesic
The finiteness of the set of branch points of a spherical mapping of a narrowing saddle surface
Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 281-286.

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We consider an oriented, finitely connected narrowing saddle surface $F\in C^2$ in $R^3$ on which the set of points of zero Gaussian curvature consists only of isolated points. It is proved that a spherical mapping of this surface can only have a finite number of branch points and the structure of the boundary of its spherical image is studied. 
@article{MZM_1972_12_3_a8,
     author = {A. L. Verner},
     title = {The finiteness of the set of branch points of a spherical mapping of a narrowing saddle surface},
     journal = {Matemati\v{c}eskie zametki},
     pages = {281--286},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a8/}
}
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A. L. Verner. The finiteness of the set of branch points of a spherical mapping of a narrowing saddle surface. Matematičeskie zametki, Tome 12 (1972) no. 3, pp. 281-286. http://geodesic.mathdoc.fr/item/MZM_1972_12_3_a8/