Geodesic
On a problem concerning the deformation of a surface with a flat point
Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 61-81 
Z. D. Usmanov. On a problem concerning the deformation of a surface with a flat point. Sbornik. Mathematics, Tome 18 (1972) no. 1, pp. 61-81. http://geodesic.mathdoc.fr/item/SM_1972_18_1_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The objects investigated are simply connected pieces of surfaces of positive curvature with isolated flat points. Infinitesimal deformations under given boundary conditions are studied. The deformation situation depends essentially on the order of tangency of the surface with its tangent plane at the flat point, as well as on the index of the boundary condition. The geometric results are based on the solution of the Riemann–Hilbert problem for generalized Cauchy–Riemann systems with singular coefficients. Bibliography: 8 titles.

[1] L. G. Mikhailov, Z. D. Usmanov, “Beskonechno malye izgibaniya poverkhnostei vrascheniya polozhitelnoi krivizny s konicheskoi ili parabolicheskoi tochkoi v polose”, DAN SSSR, 166:4 (1966), 791–794 | MR

[2] Z. D. Usmanov, “O beskonechno malykh izgibaniyakh poverkhnostei polozhitelnoi krivizny s izolirovannoi tochkoi uploscheniya”, Matem. sb., 83(125) (1970), 596–615 | MR | Zbl

[3] I. N. Vekua, Obobschennye analiticheskie funktsii, Fizmatgiz, Moskva, 1959 | MR

[4] G. S. Barkhin, V. T. Fomenko, “Ob izgibanii poverkhnostei polozhitelnoi krivizny s kraem”, Sib. matem. zh., 4:1 (1963), 32–47 | MR | Zbl

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

[6] N. V. Efimov, “Dokazatelstvo suschestvovaniya poverkhnosti neizgibaemoi “v malom””, DAN SSSR, 27 (1940), 314–317 | Zbl

[7] N. V. Efimov, “O zhestkosti v malom”, DAN SSSR, 60:5 (1948), 761–764 | MR | Zbl

[8] F. D. Gakhov, Kraevye zadachi, Fizmatgiz, Moskva, 1962