Geodesic
Deformability of surfaces of positive curvature
Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 815-823.

Voir la notice de l'article provenant de la source Math-Net.Ru

For surfaces of positive Gaussian curvature bounded away from zero the following statement is proved: A piece of a given surface containing a preassigned finite set of points and having a Lyapunov boundary can be deformed with an arbitrary given (as large as we like) bending at these points under the condition that the area of the piece is sufficiently small. 
@article{MZM_1976_19_5_a16,
     author = {S. B. Klimentov},
     title = {Deformability of surfaces of positive curvature},
     journal = {Matemati\v{c}eskie zametki},
     pages = {815--823},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a16/}
}
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S. B. Klimentov. Deformability of surfaces of positive curvature. Matematičeskie zametki, Tome 19 (1976) no. 5, pp. 815-823. http://geodesic.mathdoc.fr/item/MZM_1976_19_5_a16/