Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters - Babenko, V.I. (Журнал математической физики, анализа, геометрии, 2018)
Closed and non-closed (with planar edges) strictly convex surfaces with continuous curvatures are considered. Upper and lower bounds are obtained for the Gaussian curvature under various restrictions imposed on integral parameters of a surface: the diameter and width of the surface, the volume of the enclosed body, the maximum area of planar cross-sections of the enclosed body, the radius of a circumscribed or inscribed ball, the height of non-closed surface and the area enclosed by the planar boundary of the surface.