Geodesic
Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero
Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 501-509 
È. R. Rozendorn. Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero. Sbornik. Mathematics, Tome 44 (1983) no. 4, pp. 501-509. http://geodesic.mathdoc.fr/item/SM_1983_44_4_a7/
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     title = {Bounded complete weakly nonregular surfaces with negative curvature bounded away from zero},
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     number = {4},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In three-dimensional Euclidean space we construct a bounded saddle surface of class $C^1$, complete in its intrinsic metric. This surface has $C^\infty$ regularity everywhere except for a countable set of singular points (saddle points of the third order, isolated in the intrinsic metric). The Gaussian curvature in the sense of A. D. Aleksandrov is defined on the whole surface, is continuous and differentiable, and satisfies the inequality $K\leqslant-1$. Bibliography: 10 titles.

[1] Efimov N. V., “Vozniknovenie osobennostei na poverkhnostyakh otritsatelnoi krivizny”, Matem. sb., 64 (106) (1964), 286–320 | MR | Zbl

[2] J. Hadamard, “Les surfaces à courbures opposées et leur lignes géodesiques”, J. math. pure et appl., 5 (1898), 27–73 | Zbl

[3] Rozendorn E. R., “Postroenie ogranichennoi polnoi poverkhnosti nepolozhitelnoi krivizny”, UMN, XVI:2 (1961), 149–156 | MR

[4] Burago Yu. D., Neravenstva izoperimetricheskogo tipa v teorii poverkhnostei ogranichennoi vneshnei krivizny, Zap. nauchn. sem. LOMI AN SSSR, 10, 1968 | MR | Zbl

[5] Verner A. L., “Neogranichennost giperbolicheskogo roga v evklidovom prostranstve”, Sib. matem. zh., 11:1 (1970), 20–29 | MR | Zbl

[6] Aminov Yu. A., “Vneshnii diametr pogruzhennogo rimanova mnogoobraziya”, Matem. sb., 92 (134) (1973), 456–460 | MR | Zbl

[7] Rozendorn E. R., “O polnykh poverkhnostyakh otritsatelnoi krivizny $K \leqslant -1$ v evklidovykh prostranstvakh $E^3$ i $E^4$”, Matem. sb., 58 (100) (1962), 453–478 | MR | Zbl

[8] Efimov N. V., Kachestvennye voprosy teorii deformatsii poverkhnosti “v malom”, Trudy Matem. in-ta im. V. A. Steklova, 30, 1949 | MR | Zbl

[9] Aleksandrov A. D., Vnutrennyaya geometriya vypuklykh poverkhnostei, Gostekhizdat, M., L., 1948

[10] Rozendorn E. R., “Slabo neregulyarnye poverkhnosti otritsatelnoi krivizny”, UMN, XXI:5 (1966), 59–116 | MR