Continuous bendings of convex surfaces with boundary conditions

The author studies continuous bendings of simply connected surfaces of positive curvature, of class $C^{3,\nu}$, $0<\nu<1$, with boundary of class $C^{3,\nu}$, $0<\nu<1$, under exterior connections on the boundary (the generalized sliding condition, sleeve connections, etc.). A class of exterior connections compatible with continuous bendings of these surfaces is indicated.
Bibliography: 3 titles.