Estimates for the Gaussian Curvature of a Strictly Convex Surface and its Integral Parameters
B. Verkin Institute for Low Temperature Physics and Engineering of the National
Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
Received February 8, 2016, revised February 5, 2017.
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.
Mathematics Subject Classification 2010: 53A05.