Curvature properties of typical convex surfaces (Q1098413)

Refining and extending earlier results of himself [e.g., Math. Ann. 252, 217-219 (1980; Zbl 0427.53002)] and others, the author proves some more properties of ``typical'' convex surfaces (in the sense of Baire category). An easily formulated example says that on a typical convex curve in the plane the curvature is zero almost everywhere and infinite at an uncountable dense set of points. Higher-dimensional results deal with the behaviour of sectional curvatures in certain directions and also establish the fact a typical convex surface is, in a certain sense, almost everywhere very close to its tangent hyperplane.