A Measure Associated with a Convex Surface and Its Limit Cone

This discussion explores the measure associated with a convex surface and its limit cone. In three-dimensional Euclidean space, a convex surface at infinity tends toward a cone of rotation, referred to as the limit cone. The boundedness of the difference between the area of the convex surface and that of the limit cone is established as a whole. The proof utilizes the flat sections of the surface, formed by intersecting planes that pass through the cone’s axis of symmetry.